tag:blogger.com,1999:blog-43692631996928728082024-03-19T02:48:23.720-07:0012th-physics-importantआप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.comBlogger15125tag:blogger.com,1999:blog-4369263199692872808.post-109752262103604092012-07-14T16:46:00.000-07:002013-12-06T17:40:21.723-08:00ELECTROMAGNETIC WAVES<div dir="ltr" style="text-align: left;" trbidi="on">
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<h1 style="margin-left: 1in;">
<span style="font-size: 13pt;">ELECTROMAGNETIC WAVES </span></h1>
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<span style="font-size: 13pt;">The oscillating electric & magnetic field which regenerate each other & propagate through space with speed of light are known as electromagnetic waves.</span></div>
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<span style="font-size: 13pt;">Properties of electromagnetic waves</span></h1>
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<span style="font-size: 13pt;">1.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt;">E.M waves require no material, medium for propagation .</span></div>
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<span style="font-size: 13pt;">2.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt;">E.M waves are transverse in nature .</span></div>
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<span style="font-size: 13pt;">3.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt;">Speed of E.M wave is different in different media & is given by : ν=1/√μϵ . It is maximum in air/vacuum & equal to</span></div>
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<span style="font-size: 13pt;"> c = 1/√μ<sub>0</sub>ϵ<sub>0 </sub>=3 x 10<sup>8 </sup>m/s</span></div>
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<span style="font-size: 13pt;">4.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt;">Ratio of electric field to magnetic field gives speed .</span></div>
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<span style="font-size: 13pt;"> C=E<sub>0</sub>/B<sub>0</sub></span></div>
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<span style="font-size: 13pt;">ELECTROMAGNETIC SPECTRUM</span></h1>
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<span style="font-size: 13pt;">The orderly distribution of different type of E.M. waves according to their specific characteristic like frequency wavelength etc. is called electromagnetic spectrum .</span></div>
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<span style="font-size: 13pt;">TYPES OF E.M. WAVES</span></h1>
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<span style="font-size: 13pt;">1.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt;">Radio waves</span></div>
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<span style="font-size: 13pt;">2.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt;">Micro waves</span></div>
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<span style="font-size: 13pt;">3.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt;">Infrared waves</span></div>
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<span style="font-size: 13pt;">4.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt;">Visible rays</span></div>
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<span style="font-size: 13pt;">5.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt;">Ultraviolet rays</span></div>
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<span style="font-size: 13pt;">6.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt;">X rays</span></div>
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<span style="font-size: 13pt;">7.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt;">Gama rays.</span></div>
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<span style="font-size: 13pt;"> In ascending order of frequency for different type of waves : </span></div>
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<span style="font-size: 13pt;">Radio waves <Micro waves < Infrared waves < visible rays< ultraviolet rays < X rays < Gama rays .</span></div>
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<span style="font-size: 13pt;"> </span></div>
<h3>
<span style="font-size: 13pt;">E.M.WAVE AT A GLANCE</span></h3>
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<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><h2>
<span style="font-size: 13pt;">Types of E.M. waves</span></h2>
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<span style="font-size: 13pt;">Wavelength range</span></div>
</td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 76.95pt;" valign="top" width="103"><div class="MsoNormal">
<span style="font-size: 13pt;">Frequency range</span></div>
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<span style="font-size: 13pt;">Source</span></h2>
</td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 98.1pt;" valign="top" width="131"><div class="MsoNormal">
<span style="font-size: 13pt;">Way of detection</span></div>
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<span style="font-size: 13pt;">Applications/ effects</span></div>
</td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><h2>
<span style="font-size: 13pt;">Radio waves</span></h2>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 90.9pt;" valign="top" width="121"><div class="MsoNormal">
<span style="font-size: 13pt;">Greater than 10cm</span></div>
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<span style="font-size: 13pt;">500kHz to 1000mHz</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 93.15pt;" valign="top" width="124"><div class="MsoNormal">
<span style="font-size: 13pt;">Rapid acceleration & deacceleration of electrons</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 98.1pt;" valign="top" width="131"><div class="MsoNormal">
<span style="font-size: 13pt;">Reciver aerial</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 94.95pt;" valign="top" width="127"><div class="MsoNormal">
<span style="font-size: 13pt;">Radio & TV communication</span></div>
</td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><h2>
<span style="font-size: 13pt;">Micro waves</span></h2>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 90.9pt;" valign="top" width="121"><div class="MsoNormal">
<span style="font-size: 13pt;">1mm to10 cm</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 76.95pt;" valign="top" width="103"><div class="MsoNormal">
<span style="font-size: 13pt;">10<sup>9</sup>to 10<sup>12</sup>Hz</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 93.15pt;" valign="top" width="124"><div class="MsoNormal">
<span style="font-size: 13pt;">Klystron valve Magnetron valve</span></div>
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<span style="font-size: 13pt;">Point contact diodes</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 94.95pt;" valign="top" width="127"><div class="MsoNormal">
<span style="font-size: 13pt;">Used in radar system</span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">Micro wave oven</span></div>
</td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal">
<span style="font-size: 13pt;">Infrared waves</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 90.9pt;" valign="top" width="121"><div class="MsoNormal">
<span style="font-size: 13pt;">700nm to 1mm</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 76.95pt;" valign="top" width="103"><div class="MsoNormal">
<span style="font-size: 13pt;">10<sup>12</sup> to 4x10<sup>14</sup>Hz</span></div>
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<span style="font-size: 13pt;">Vibration of atoms & moleculs</span></div>
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<span style="font-size: 13pt;">Thermoriles</span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">Bolometers</span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">Infraphotographic film</span></div>
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<span style="font-size: 13pt;">Cause heating effect</span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">Physical therapy</span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">Remote switches </span></div>
</td> </tr>
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<span style="font-size: 13pt;">Visible rays</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 90.9pt;" valign="top" width="121"><div class="MsoNormal">
<span style="font-size: 13pt;">400nmto 700nm</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 76.95pt;" valign="top" width="103"><div class="MsoNormal">
<span style="font-size: 13pt;">4x10<sup>14</sup> to7x10<sup> 14</sup>Hz</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 93.15pt;" valign="top" width="124"><div class="MsoNormal">
<span style="font-size: 13pt;">Electrons in atoms emit light when they move from one energy level to lower energy level</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 98.1pt;" valign="top" width="131"><div class="MsoNormal">
<span style="font-size: 13pt;">The eye, photo cell & </span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">Photographic films</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 94.95pt;" valign="top" width="127"><div class="MsoNormal">
<span style="font-size: 13pt;">To see objects</span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">To convert in electric energy</span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">To take photographs optical signal</span></div>
</td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal">
<span style="font-size: 13pt;">Ultraviolet waves</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 90.9pt;" valign="top" width="121"><div class="MsoNormal">
<span style="font-size: 13pt;">6x10<sup>-10</sup>m to 400nm</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 76.95pt;" valign="top" width="103"><div class="MsoNormal">
<span style="font-size: 13pt;">7x10<sup>14</sup>to5x10<sup>17</sup>Hz</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 93.15pt;" valign="top" width="124"><div class="MsoNormal">
<span style="font-size: 13pt;">Inner shell electron in atom moving from one energy level to lower energy level</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 98.1pt;" valign="top" width="131"><div class="MsoNormal">
<span style="font-size: 13pt;">Photocell Photographic films</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 94.95pt;" valign="top" width="127"><div class="MsoNormal">
<span style="font-size: 13pt;">LASIK eye surgery &</span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">To kill germs</span></div>
<div class="MsoNormal">
<br /></div>
</td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal">
<span style="font-size: 13pt;">X rays</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 90.9pt;" valign="top" width="121"><div class="MsoNormal">
<span style="font-size: 13pt;">10<sup>-3</sup>nm to1nm</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 76.95pt;" valign="top" width="103"><div class="MsoNormal">
<span style="font-size: 13pt;">3x10<sup>16</sup>to 3x10<sup>20</sup>Hz</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 93.15pt;" valign="top" width="124"><div class="MsoNormal">
<span style="font-size: 13pt;">X ray tube or innershell electron</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 98.1pt;" valign="top" width="131"><div class="MsoNormal">
<span style="font-size: 13pt;">Photographic film Geiger tubes Ionisation chamber</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 94.95pt;" valign="top" width="127"><div class="MsoNormal">
<span style="font-size: 13pt;">Diagnostic measure,</span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">Treatment of cancer &</span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">To locate the fracture of bones</span></div>
</td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal">
<span style="font-size: 13pt;">Gama rays</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 90.9pt;" valign="top" width="121"><div class="MsoNormal">
<span style="font-size: 13pt;">Less than 10<sup>-4</sup>to10<sup>-10</sup>m</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 76.95pt;" valign="top" width="103"><div class="MsoNormal">
<span style="font-size: 13pt;">Greater than 3x10<sup>20</sup>or10<sup>19</sup>Hz</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 93.15pt;" valign="top" width="124"><div class="MsoNormal">
<span style="font-size: 13pt;">Radioactive decay of nucleus</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 98.1pt;" valign="top" width="131"><div class="MsoNormal">
<span style="font-size: 13pt;">Photographic film Geiger tubes Ionisation chamber</span></div>
</td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 94.95pt;" valign="top" width="127"><div class="MsoNormal">
<span style="font-size: 13pt;">To destroy cancer cells</span></div>
<div class="MsoNormal">
<span style="font-size: 13pt;">Experimental study</span></div>
</td> </tr>
</tbody></table>
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<span style="font-size: 13pt;"> “ <b>Electromagnetic wave”2</b></span></div>
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<b><span style="font-size: 13pt; line-height: 150%;">1</span></b><span style="font-size: 13pt; line-height: 150%;">-State any four properties of electromagnetic waves ?</span></div>
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<b><span style="font-size: 13pt; line-height: 150%;">2</span></b><span style="font-size: 13pt; line-height: 150%;">-Arrange following radiation is the descending order of the wavelength ?</span></div>
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<b><span style="font-size: 13pt; line-height: 150%;"> Gama </span></b><span style="font-size: 13pt; line-height: 150%;">rays , infrared rays microwaves , yellow light , radio waves . </span></div>
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<span style="font-size: 13pt; line-height: 150%;"> <b>3</b>-write an expression for speed of electromagnetic waves in free space . </span></div>
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<span style="font-size: 13pt; line-height: 150%;"> 4-give one use of following .-</span></div>
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<span style="font-size: 13pt; line-height: 150%;">a.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">infrared rays </span></div>
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<span style="font-size: 13pt; line-height: 150%;">b.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">gamma rays </span></div>
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<span style="font-size: 13pt; line-height: 150%;">c.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">microwaves </span></div>
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<span style="font-size: 13pt; line-height: 150%;">d.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">ultraviolet radiation .</span></div>
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<b><span style="font-size: 13pt; line-height: 150%;"> 5</span></b><span style="font-size: 13pt; line-height: 150%;">-Deduce an expression for the distance which the T.V. signal can directly be received from a T.V. tower of height .</span></div>
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<b><span style="font-size: 13pt; line-height: 150%;">6</span></b><span style="font-size: 13pt; line-height: 150%;">- By which way the X- rays and gamma rays can be produce and detected write one use of each . </span></div>
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<span style="font-size: 13pt; line-height: 150%;">7- What oscillate in E.M. Waves? Give four example of E.M. waves .</span></div>
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<b><span style="font-size: 13pt; line-height: 150%;">8</span></b><span style="font-size: 13pt; line-height: 150%;">.- identify the part of the electromagnetic spectrum which is </span></div>
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<span style="font-size: 13pt; line-height: 150%;">a.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">Suitable for radar system used in air craft navigation </span></div>
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<span style="font-size: 13pt; line-height: 150%;">b.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">Which is adjacent to low frequency end of the E.M. spectrum . </span></div>
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<span style="font-size: 13pt; line-height: 150%;">c.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">Produced in nuclear reaction </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 1in; text-align: justify; text-indent: -0.25in;">
<span style="font-size: 13pt; line-height: 150%;">d.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">produced by bombarding a metal target by high speed electron </span></div>
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<span style="font-size: 13pt; line-height: 150%;"> <b>9-</b> Name the radiation of the electromagnetic spectrum which are used in </span></div>
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<span style="font-size: 13pt; line-height: 150%;">1.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">War far to look through fog.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 117pt; text-align: justify; text-indent: -0.25in;">
<span style="font-size: 13pt; line-height: 150%;">2.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">Radar of geostationary satellite </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 117pt; text-align: justify; text-indent: -0.25in;">
<span style="font-size: 13pt; line-height: 150%;">3.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">studying the structure and properties of atom and molecules </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 117pt; text-align: justify; text-indent: -0.25in;">
<span style="font-size: 13pt; line-height: 150%;">4.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">Killing germs.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 117pt; text-align: justify; text-indent: -0.25in;">
<span style="font-size: 13pt; line-height: 150%;">5.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">To take photograph of internal part of human body.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 117pt; text-align: justify; text-indent: -0.25in;">
<span style="font-size: 13pt; line-height: 150%;">6.<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 13pt; line-height: 150%;">To produce intense heating effect.</span></div>
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<span style="font-size: 13pt; line-height: 150%;"> <b> 10</b> – why sky wave are not used in transmission of T.V. signal .Why the transmission of the signal using sky wave is restricted to up to 30 MHz .</span></div>
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आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com1tag:blogger.com,1999:blog-4369263199692872808.post-60704235390984087192012-07-14T03:51:00.000-07:002013-12-06T17:38:46.855-08:00Dual nature of radiation and matter<div dir="ltr" style="text-align: left;" trbidi="on">
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<b><span style="font-size: 18pt;"> </span><span style="color: green; font-size: 16pt; line-height: 31px;">Photo electric emission</span><span style="color: green; font-size: 16pt; line-height: 31px;">-</span><span style="font-size: 16pt; line-height: 31px;"> </span></b></h2>
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<span style="font-size: 16pt; line-height: 31px;"></span>when light of suitable frequency is incident on a metal surface, electrons are emitted from the metal surface. The emitted electrons are called <b>photoelectrons</b> and this phenomenon is called <b>photo electric emission.<span style="font-size: 10pt; line-height: 19px;"> </span></b></div>
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<b><span style="color: green; font-size: 16pt; line-height: 31px;"> Einstein’s photo electric equation</span><span style="color: green;">:</span> </b></div>
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Let a photon of frequency ν having energy <b>hν </b>is incident on the metal surface. The energy of photon divided into two parts-</div>
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<li class="MsoNormal" style="line-height: 24px;">One part of this energy is absorbed exceed the minimum energy needed for the electron escape from the metal. This energy is called work function of metal and is denoted by <b>ω<sub>o </sub></b>and frequency of this energy is called threshold frequency and <b><i><u><span style="color: red;">ω<sub>o</sub>= hν<sub>o</sub></span><sub></sub></u></i></b></li>
<li class="MsoNormal" style="line-height: 24px; text-align: justify;">The second part of photon energy is used to accelerate the free electron i.e. in the form of kinetic energy.</li>
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Therefore- <b><i><span style="color: red;">hν = ω<sub>o + K.E.</sub></span></i></b></div>
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<b><i><sub><span style="color: red;"> </span></sub><span style="color: red;">hν = hν<sub>o </sub>+ K.E.</span></i></b></div>
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<b><i><u><span style="color: red;">K.E. = hν - hν<sub>o</sub></span></u></i></b><sub><span style="color: red;"></span></sub></div>
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This is called Einstein’s photo<span style="font-size: 10pt; line-height: 19px;"> </span>electric equation.<span style="font-size: 10pt; line-height: 19px;"> </span></div>
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<span style="color: green; font-size: 16pt; line-height: 31px;"> Particle nature of light</span><span style="color: green;">:</span><span style="font-size: 10pt; line-height: 19px;"> </span> </div>
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Electromagnetic radiation follows particle nature as photon as below-</div>
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<li class="MsoNormal" style="line-height: 24px;">An interaction of radiation with matter, radiation behaves as if it is made up of particle called photons</li>
<li class="MsoNormal" style="line-height: 24px;">Each photon has energy <b>E = hν,</b> <b>momentum = hν/c</b> and speed <b>c (speed of light</b> )</li>
<li class="MsoNormal" style="line-height: 24px;">All photons of light of a particular frequency<b> ν</b> or wavelength <b>λ, </b>have the same energy</li>
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<b><span style="color: red;"> E = hν = hc/λ</span></b></div>
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<b><span style="color: red;"> </span></b> and momentum</div>
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<b><span style="color: red;">p = hν/c =h/λ</span></b></div>
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<li class="MsoNormal" style="line-height: 24px;">Photon energy is independent of intensity of radiation</li>
<li class="MsoNormal" style="line-height: 24px;">Photons are electrically neutral and not deflected by electric and magnetic field.</li>
<li class="MsoNormal" style="line-height: 24px;">In a photon particle collision the total energy and total momentum are conserved but number of photon may not be conserved.</li>
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<b><span style="font-size: 10pt;"> </span><span style="color: green; font-size: 16pt;">Wave nature of matter</span><span style="color: green; font-size: 16pt;">-</span><span style="font-size: 16pt;"></span></b></div>
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<span style="font-size: 10pt; line-height: 19px;"> According to de-Broglie, Moving particle of matter should display wave like properties under suitable</span></div>
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<span style="font-size: 10pt; line-height: 19px;"> conditions. The wavelength <b>λ </b>associated with a particle momentum<b> p</b> is given as-</span></div>
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<span style="font-size: 10pt; line-height: 19px;"> <b><span style="color: red;">λ = h/p = h/mv </span></b></span></div>
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<span style="font-size: 10pt; line-height: 19px;"> Where m is the mass of the particle and v is speed of particle. <b>ν</b> is called <b>de-Broglie wavelength</b>.</span></div>
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<span style="font-size: 10pt; line-height: 19px;"> </span><span style="color: green; font-size: 16pt; font-weight: normal; line-height: 31px;">de-Broglie wave length of electron</span><span style="color: green; font-weight: normal;">-</span><span style="font-weight: normal;"> </span></h3>
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Consider an electron of mass m, charge e accelerated from rest through a potential <b>V</b>. The kinetic energy<b> K</b> of the electron equals the work done (<b>eV</b>) on it by the electric field:<u> </u></div>
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<b> K =eV</b></div>
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Now <b> K = 1/2mv<sup>2</sup> = p<sup>2</sup>/2m</b></div>
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<b> </b></div>
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<b>P =√2mK</b></div>
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<b> = √2m eV </b></div>
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Therefore the de-Broglie wavelength λ of the electron is given by</div>
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<b>λ = h/p = h/√2mK = h/√2m eV</b></div>
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Putting the value of <b>h, m,</b> and <b>e</b> we get</div>
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<b><i><span style="color: red;">λ = 1.227/√v nm</span> </i></b> where v is the magnitude of accelerating potential in volts.</div>
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<b><span style="color: green; font-size: 16pt; line-height: 31px;"> Uncertainty principle</span><span style="color: green;">:-</span></b></div>
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It is not possible to determine the position and momentum of any particle at the same time exactly. If there is uncertainty in position is<b> Δx</b> and in momentum <b>Δp</b> then</div>
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<b><i> <span style="color: red;">Δx. Δp ≈h/2Π</span></i></b></div>
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<b><span style="color: green; font-size: 16pt; line-height: 31px;"> Davisson and Germer Experiment</span><span style="font-size: 16pt; line-height: 31px;"></span><span style="font-size: 10pt; line-height: 19px;"></span></b></h3>
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The wave nature of electron<u><span style="color: green;"> </span></u>was first experimentally verified by C.J. Davidson and L.H. Germer in 1927 and independently by J.J.Thomson in 1928, who observed diffraction effects which beam of electrons scattered by crystals.</div>
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Experimental arrangement as below-</div>
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Here electron beam emitted by the filament F with the help of L.T. Battery and this beam is accelerated with the help of H.T. Battery. The electron beam fall on the nickel crystal. The electron are scattered in all directions by the atom of the crystal.</div>
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The intensity of the electron beam, scattered in a given direction is measured by the electron detector. The detector can be moved on a circular scale and is connected to a sensitive galvanometer which records the current. The intensity of the scattered electron beam is measured for different values of angle of scattering and which is the angle b/w the incident and the scattering electric beams. The variation of intensity (<b>I</b>) of the scattered electron with the angle of scattering and is obtained for different accelerating voltages.</div>
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The experiment was performed by varying the accelerating voltage from 44V to 68V .</div>
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It is observed that maximum value of (I) of the scattered electron for an accelerating voltage of 54V at a scattering angle θ = 50<sup>0</sup></div>
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The wavelength of matter wave is associated with electron in experimentally obtained <b><u>λ </u> <u>= 0.165 nm </u>------------------</b> <b>(1)</b></div>
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The <b>de-Brogli wavelength λ</b> associated with electron using <b>λ = h/p =1.227/<i>√</i>v nm.</b> For<b> V=54V</b></div>
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<b> λ = 1.227/<i>√</i>54 nm.</b></div>
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<b><u>λ = 0.167 nm.</u>-------------------- (2)</b></div>
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From experimental result and calculated result we see that both are approximately same. This shows that matter wave associated with moving electron.</div>
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<b><u><span style="color: red; font-size: 16pt;">Important Questions:-</span></u></b><span style="color: red;"><u></u></span></div>
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<li class="MsoNormal" style="line-height: 24px;"><span style="font-size: 11pt; line-height: 22px;">Define work function function for a given metallic surface?</span></li>
<li class="MsoNormal" style="line-height: 24px;"><span style="font-size: 11pt; line-height: 22px;">Two metals <b>m<sub>1</sub></b> & <b>m<sub>2</sub></b> have work functions <b>2 eV</b> and <b>4 eV</b> respectively. Which of the two has a higher threshold wavelength for photo electric emission?</span></li>
<li class="MsoNormal" style="line-height: 24px;"><span style="font-size: 11pt; line-height: 22px;">A photon has velocity ‘<b>C</b>’ and frequency <b><i>v</i>.</b> write down the expression for its wavelength?</span></li>
<li class="MsoNormal" style="line-height: 24px;"><span style="font-size: 11pt; line-height: 22px;">On what factor does the energy carried by a photon of light depend?</span></li>
<li class="MsoNormal" style="line-height: 24px;"><span style="font-size: 11pt; line-height: 22px;">Name the experiment which establishes the wave nature of a particle?</span></li>
<li class="MsoNormal" style="line-height: 24px;"><span style="font-size: 11pt; line-height: 22px;">A photon and an electron have the same wavelength. Which particle is moving faster?</span></li>
<li class="MsoNormal" style="line-height: 24px;"><span style="font-size: 11pt; line-height: 22px;">What is the de-Broglie wavelength of a 3 <b>Kg </b>object moving with a speed of 2 <b>m/s</b>?</span></li>
<li class="MsoNormal" style="line-height: 24px;"><span style="font-size: 11pt; line-height: 22px;">Explain laws of photoelectric emission on the basis of Einstein’s photo electric equation?</span></li>
<li class="MsoNormal" style="line-height: 24px;"><span style="font-size: 11pt; line-height: 22px;">What is photoelectric effect? Calculate the threshold frequency of photon for photoelectric emission from a metal of work function 0.1<b> eV</b>?</span></li>
<li class="MsoNormal" style="line-height: 24px;"><span style="font-size: 11pt; line-height: 22px;">what is the-</span></li>
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<span style="color: red; font-size: 11pt; line-height: 22px;">·<span style="font-size: 7pt; line-height: normal;"> </span></span><span style="font-size: 11pt; line-height: 22px;">momentum</span></div>
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<span style="color: red; font-size: 11pt; line-height: 22px;">·<span style="font-size: 7pt; line-height: normal;"> </span></span><span style="font-size: 11pt; line-height: 22px;">speed and</span></div>
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<span style="color: red; font-size: 11pt; line-height: 22px;">·<span style="font-size: 7pt; line-height: normal;"> </span></span><span style="font-size: 11pt; line-height: 22px;">de-Broglie wavelength of an electron with kinetic energy of 120 <b>eV</b>?</span></div>
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<ol start="11" style="font-family: Arial, Helvetica, sans-serif; margin-top: 0in;" type="1">
<li class="MsoNormal" style="line-height: 24px;"><span style="font-size: 11pt; line-height: 22px;">Describe deviation and Germer experiment to establish the wave nature of electrons. Draw a labeled diagram of the apparatus used.</span></li>
<li class="MsoNormal" style="line-height: 24px;"><b><span style="color: red; font-size: 11pt; line-height: 22px;">a.</span></b><span style="font-size: 11pt; line-height: 22px;"> Define terms-</span></li>
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<span style="color: red; font-size: 11pt; line-height: 22px;">·<span style="font-size: 7pt; line-height: normal;"> </span></span><span style="font-size: 11pt; line-height: 22px;">Work function</span></div>
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<span style="color: red; font-size: 11pt; line-height: 22px;">·<span style="font-size: 7pt; line-height: normal;"> </span></span><span style="font-size: 11pt; line-height: 22px;">Threshold frequency</span></div>
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<span style="color: red; font-size: 11pt; line-height: 22px;">·<span style="font-size: 7pt; line-height: normal;"> </span></span><span style="font-size: 11pt; line-height: 22px;">Stopping potential with reference to photoelectric effect.</span></div>
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<b><span style="color: red; font-size: 11pt; line-height: 22px;"> b.</span></b><b><span style="font-size: 11pt; line-height: 22px;"> </span></b><span style="font-size: 11pt; line-height: 22px;">Calculate the maximum kinetic energy of electrons emitted from a photo sensitive surface a work function 3.2<b> eV</b> for the incident radiation of wave length 300 <b>nm.</b></span></div>
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आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0tag:blogger.com,1999:blog-4369263199692872808.post-3742687202003409502012-06-16T17:06:00.000-07:002012-06-16T17:06:55.271-07:00Current & Electricity<div dir="ltr" style="text-align: left;" trbidi="on"><div style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><b><u>Relation b/w Electric current & Drift velocity :-</u></b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">Let “E” be the electric field applied across a conductor of length “l” & cross sectional area “A” .Suppose the number of free electrons per unit volume of the conductor is “n” .</span></div><div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ9r5wEUUPLeFVi5-yoktzs1nRl0ygCesVXGvN0q_BIxoJ5gl-Kggk_eW_NrZ7a5WQnF3O2E7ACSywTiiRlR5Tcd7TEzS4QfdCa9j9HGO3AtIJBdj-YC52LqAKkRd1WkoulnCxVDNPLjGN/s1600/New+Picture.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="161" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ9r5wEUUPLeFVi5-yoktzs1nRl0ygCesVXGvN0q_BIxoJ5gl-Kggk_eW_NrZ7a5WQnF3O2E7ACSywTiiRlR5Tcd7TEzS4QfdCa9j9HGO3AtIJBdj-YC52LqAKkRd1WkoulnCxVDNPLjGN/s400/New+Picture.png" width="400" /></a></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div align="center" class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: center;"></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> Then total number of electron in the conductor = n (A .l)</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> Now , total charge within the conductor</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> q = total number of electrons X charge of each electron</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> q = n A l X e</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> or q = n e A l </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> therefore time taken by the electron to cover the length “l” is</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> length of the conductor </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;">t = ---------------------------------</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;"> drift velocity</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;"> l</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;">t = ---------------</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;"> v<sub>d</sub></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;"> </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;">Now the current flowing through the conductor is </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;"> q n e A l</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;">I = ------------- = --------------- = n e A v<sub>d</sub></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;"> t l/v<sub>d</sub></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;"><span style="height: 3px; left: 0px; margin-left: 167px; margin-top: 6px; position: absolute; width: 242px; z-index: 251656192;"><img height="3" src="file:///C:%5CDOCUME%7E1%5CAMITGA%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image003.gif" width="242" /></span><span style="height: 50px; left: 0px; margin-left: 407px; margin-top: 6px; position: absolute; width: 2px; z-index: 251659264;"><img height="50" src="file:///C:%5CDOCUME%7E1%5CAMITGA%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image004.gif" width="2" /></span><span style="height: 50px; left: 0px; margin-left: 167px; margin-top: 6px; position: absolute; width: 2px; z-index: 251657216;"><img height="50" src="file:///C:%5CDOCUME%7E1%5CAMITGA%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image004.gif" width="2" /></span>hence<sub> </sub></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: small;"> I = n e A v<sub>d</sub></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.5in; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><span style="position: relative; z-index: 251658240;"><span style="height: 2px; left: 167px; position: absolute; top: -1px; width: 242px;"><img height="2" src="file:///C:%5CDOCUME%7E1%5CAMITGA%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image005.gif" width="242" /></span></span> </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">Resistivity or Specific resistivity :- From the relation </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> l</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> R = ρ---------------- </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> A</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> R X A</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">We have resistivity ρ = -----------------</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> l </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">If “l” = 1 unit , A = 1 unit </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
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</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">Then ρ = R </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">Hence resistivity is numerically equal to the resistence of a conductor having unit length & unit area of cross section . </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">It is the property of the material of the conductor .</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">Its S.I. unit is Ohm-meter (Ω-m).</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">Conductivity(σ ) :- It is defined as the reciprocal of resistivity . So </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> 1</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">Conductivity σ =---------------------------</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> Resistivity </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">Its S.I unit is 1/ Ohm –meter = (Ω-m)<sup>-1</sup></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><sup> </sup></span> </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><b>Temperature dependence of Resistivity </b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">The resistivity of conductor is increased with temperature , while in case semiconductors & insulators ,the resistivity decreases with increasing temperature </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><b>Colour code for carbon resistors:-</b>Carbon resistors have four bands or rings of different colours.the first two bands indicates the decimal multiplier. The fourth and last band indicates the tolerance.</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">The following table gives the colour code for carbon resistors </span></div><table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: medium none; font-family: Arial,Helvetica,sans-serif;"><tbody>
<tr style="height: 13.4pt;"> <td style="border: 1pt solid windowtext; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;"><b>Colour </b></span></div></td> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;"><b>Number </b></span></div></td> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;"><b>Multiplier</b></span></div></td> </tr>
<tr style="height: 13.4pt;"> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: -moz-use-text-color windowtext windowtext; border-right: 1pt solid windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">Black </span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">0</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">10<sup>0</sup>or 1</span></div></td> </tr>
<tr style="height: 13.4pt;"> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: -moz-use-text-color windowtext windowtext; border-right: 1pt solid windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">Brown </span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">1</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">10<sup>1</sup></span></div></td> </tr>
<tr style="height: 13.4pt;"> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: -moz-use-text-color windowtext windowtext; border-right: 1pt solid windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">Red </span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">2</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">10<sup>2</sup></span></div></td> </tr>
<tr style="height: 13.4pt;"> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: -moz-use-text-color windowtext windowtext; border-right: 1pt solid windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">Orange</span> </div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">3</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">10<sup>3</sup></span></div></td> </tr>
<tr style="height: 14.15pt;"> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: -moz-use-text-color windowtext windowtext; border-right: 1pt solid windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 14.15pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">Yellow </span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 14.15pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">4</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 14.15pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">10<sup>4</sup></span></div></td> </tr>
<tr style="height: 13.4pt;"> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: -moz-use-text-color windowtext windowtext; border-right: 1pt solid windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">Green </span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">5</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">10<sup>5</sup></span></div></td> </tr>
<tr style="height: 13.4pt;"> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: -moz-use-text-color windowtext windowtext; border-right: 1pt solid windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">Blue</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">6</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">10<sup>6</sup></span></div></td> </tr>
<tr style="height: 13.4pt;"> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: -moz-use-text-color windowtext windowtext; border-right: 1pt solid windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">Violet</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">7</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">10<sup>7</sup></span></div></td> </tr>
<tr style="height: 13.4pt;"> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: -moz-use-text-color windowtext windowtext; border-right: 1pt solid windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">Gray </span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">8</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 13.4pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">10<sup>8</sup></span></div></td> </tr>
<tr style="height: 14.15pt;"> <td style="-moz-border-bottom-colors: none; -moz-border-image: none; -moz-border-left-colors: none; -moz-border-right-colors: none; -moz-border-top-colors: none; border-color: -moz-use-text-color windowtext windowtext; border-right: 1pt solid windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 14.15pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">white</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 14.15pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">9</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 14.15pt; padding: 0in 5.4pt; width: 85.95pt;" valign="top" width="115"><div class="MsoNormal"><span style="font-size: small;">10<sup>9</sup></span></div></td> </tr>
</tbody></table><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><b>Tolerance (%):</b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><b>GOLD ± 5%</b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><b>SILVER ± 10%</b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><b>NO COLOR ±20%</b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">EX:-If the four colors are yellow ,orange ,blue & gold, the resistance value will be : 43X10<sup>6 </sup>± 5%.</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><sup> </sup></span> </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><b>Kirchhoff’s rule</b> ---First rule or Junction rule It states that the algebraic sum of all the junction is Zero .</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">Ex- The current entering the junction are taken as positive & the current leaving the junction are taken as negative . </span></div><div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixc6N2aNi581vMc9EjJmdPFQJqIZWiqTuC_5OSBQZgOb8f0jYd_ZCCJh3o2smKP6diTKyK68kkZxwK5D5p3s3phcBz_1tO2pnnBe2o7-0I6FwXSPHm1hkTVhpANAgTeIcYqwj7EY67wx2X/s1600/New+Picture+%281%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixc6N2aNi581vMc9EjJmdPFQJqIZWiqTuC_5OSBQZgOb8f0jYd_ZCCJh3o2smKP6diTKyK68kkZxwK5D5p3s3phcBz_1tO2pnnBe2o7-0I6FwXSPHm1hkTVhpANAgTeIcYqwj7EY67wx2X/s400/New+Picture+%281%29.png" width="400" /></a></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div align="center" class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: center;"><span style="font-size: small;"></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">From the given figure applying kirchhoff’s rule we get </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">I<sub>1</sub> - I<sub>2</sub> + I<sub>3</sub> + I<sub>4</sub> - I<sub>5</sub> + I<sub>6</sub> = 0</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> </span> </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"><b>Kirchhoff’s IInd law or loop law ----</b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">The algebraic sum of changes in potential around any closed loop involving resistors & cells in the loop is zero .</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">Sign convention –</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: small;">(i)<span style="-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>The e.m.f. of a cell is taken negative if one moves in the direction of increasing potential (i.e. from –ve pole to + ve pole ) through the cell & is taken positive if one moves in the direction of decreasing potential ( from +ve pole to –ve pole) trough the cell . It means while traversing a loop if –ve pole of the cell is incountered first then its e.m.f. is negative otherwise positive .</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: small;">(ii)<span style="-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>The product of resistence & current in an arm of the circuit is taken +ve if the direction of the current in that arm is in the same sense as one moves in a closed path & taken –ve if the direction of current in that arm is opposite to the sense as one moves in a closed path .</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.75in; text-indent: -0.5in;"><br />
</div><div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_zGemq9oYO5IxxTov2j7CAB6Hm0bFWPlQqaNd5QBg9N8xLwkhio0zzfKXZM6mFFhp8UWw5R0VEys4M1i6p2jH-niW-5iB0P672EQqoP_iI7sW_Ndl99TE6zxKwYpO9P6ieuKkyAG513iO/s1600/New+Picture+%282%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="203" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_zGemq9oYO5IxxTov2j7CAB6Hm0bFWPlQqaNd5QBg9N8xLwkhio0zzfKXZM6mFFhp8UWw5R0VEys4M1i6p2jH-niW-5iB0P672EQqoP_iI7sW_Ndl99TE6zxKwYpO9P6ieuKkyAG513iO/s400/New+Picture+%282%29.png" width="400" /></a></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: small;">(iii)<span style="-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> We can traverse in aclosed path of a circuit in aclockwise or anticlockwise direction.</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;">Ex- Applying kirchoff’s IInd rule in aclosed loop ABEFA </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> I<sub>3</sub> R <sub>2</sub> + I<sub>1</sub> R <sub>1</sub> - E<sub>1</sub> = 0</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> E<sub>1</sub> = I<sub>3</sub> R <sub>2</sub> + I<sub>1</sub> R <sub>1</sub> </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">Similarly for closed loop BCDEB -</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> I<sub>3</sub> R <sub>2</sub> + I<sub>2</sub> R 3 - E<sub>2</sub> = 0</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> E<sub>2</sub> = I<sub>3</sub> R <sub>2</sub> + I<sub>2</sub> R 3 </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;"> </span> </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"><b>Wheat stone bridge – it is an application of kirchhoff’s law .</b></span></div><div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9bVOAp2g_Jb5TetWSsglhU1FWi-hLycFpFHKC4qkRXZH4t4QTgirmqUABHV03cWQqPopOq6HCUtr3BCJQKJkWcS6CJHZdv6bNkL_fSk5MqhMhHv34oDdeFT9yOE17SBgsoamJvhLV-MSv/s1600/New+Picture+%283%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="376" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9bVOAp2g_Jb5TetWSsglhU1FWi-hLycFpFHKC4qkRXZH4t4QTgirmqUABHV03cWQqPopOq6HCUtr3BCJQKJkWcS6CJHZdv6bNkL_fSk5MqhMhHv34oDdeFT9yOE17SBgsoamJvhLV-MSv/s400/New+Picture+%283%29.png" width="400" /></a></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div align="center" class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in; text-align: center;"><span style="font-size: small;"></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;">Wheat stone bridge consists of four resistance P,Q,R &S connected in a different arms of a quadrilateral ABCD . cA source of EMF & key is connected along one of the diagonal & a galvanometer is connected along another diagonal . </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> In the case of a balanced bridge , there is no current through the galavanometer i.e. I<sub>g </sub> = 0</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;">Then P/Q =R/S</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;">Proof – </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;">Applying kirchhoff’s IInd law in the closed loop ABDA </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> <sub> </sub> I<sub>1 </sub>P - (I-I<sub>1 </sub>) R = 0</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> <sub> </sub> I<sub>1 </sub>P = (I-I<sub>1 </sub>) R ------------------------(1)</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;">Applying kirchhoff’s IInd law in the closed loop BCDB</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> I<sub>1 </sub>Q - (I-I<sub>1 </sub>) S = 0</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> I<sub>1 </sub>P = (I-I<sub>1 </sub>) R ---------------(2)</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;">Dividing eq (1) by (2) –</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> I<sub>1 </sub>P (I-I<sub>1 </sub>) R</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;">---------------- = -------------------- </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> I<sub>1 </sub>Q (I-I<sub>1 </sub>) S</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: small;"> P/Q = R/S hp </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.25in;"><span style="font-size: 14pt;"> </span> </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"><b><u><span style="color: red;">QUESTION</span></u></b><span style="color: red;">:- </span>In the fig different resistors are connected. Find the net current drawn from the cell.</span></div><div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-QhdROXnxtAQC78LwZhtdpCie8LezCyryK1KchBvIBzPfHoU8XWjfenkjM3mqUDUFpBZtbZ9XQrgOdwGgFvCeHN6J4ez1dxVsp8fLnhHFL86_CjOTiMS7YvOgwOEwWGkEsH70fvQn-W1U/s1600/New+Picture+%284%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="315" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-QhdROXnxtAQC78LwZhtdpCie8LezCyryK1KchBvIBzPfHoU8XWjfenkjM3mqUDUFpBZtbZ9XQrgOdwGgFvCeHN6J4ez1dxVsp8fLnhHFL86_CjOTiMS7YvOgwOEwWGkEsH70fvQn-W1U/s320/New+Picture+%284%29.png" width="320" /></a></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><br />
</div><div align="center" class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: center;"></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"><b><u><span style="color: red;">SOLUTION</span></u></b><span style="color: red;">:-</span> In the given diagram </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> According to the balanced condition of WHEAT STONE BRIDGE</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">P/Q =R/S</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">2/4 = 3/6 =1/2</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">So, the bridge is balanced & there will be no current through the 5Ω resistor.</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"><u>To find the equivalent resistance between A& C</u>:-</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> Since 2Ω &4Ω are connected in series.</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> R<sub>ABC</sub> = R<sub>AB </sub>+ R<sub>BC</sub></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> = 2Ω + 4Ω</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> = 6Ω </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">Again 3Ω & 6Ω are connected in series </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> R<sub>ADC</sub> = R<sub>AD </sub>+ R<sub>DC</sub></span> </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> = 3Ω + 6Ω</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">= 9Ω</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">Now these resistances of 6Ω & 9Ω are connected in parallel. So, the equivalent resistances between A& C is</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">1/ R<sub>AC</sub> = 1/6+1/9</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> = 18/5</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> =3•6Ω</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">So,the equivalent resistance of the circuit is </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">R = 3•6Ω + 2∙4Ω = 6Ω </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">Hence, the current drawn from the cell is </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">I = 12Ω/6Ω</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">= 2Amp</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> </span> </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"><b><u>METER BRIDGE OR SLIDE WIRE BRIDGE </u>:- </b>It is the practical application of Wheat stone bridge. It consist of a wire of length 1m & uniform cross-sectional area.</span></div><div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIK9T2pfCHHfuvGyM8c1STM7-QVBPWhQFGbvTrOnMMeUIaEZDpzx6JjBuTXeF1TVBrgTFlkWzroLjMq22Ah7fIswCjDsjmGD_FOF9rKz6TBG1b0CNngbsToggHA2EVqvUKDzqWd7e4B9CS/s1600/New+Picture+%285%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="195" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIK9T2pfCHHfuvGyM8c1STM7-QVBPWhQFGbvTrOnMMeUIaEZDpzx6JjBuTXeF1TVBrgTFlkWzroLjMq22Ah7fIswCjDsjmGD_FOF9rKz6TBG1b0CNngbsToggHA2EVqvUKDzqWd7e4B9CS/s320/New+Picture+%285%29.png" width="320" /></a></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><br />
</div><div align="center" class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: center;"></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;">From the condition of balanced Wheat stone bridge</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> R/S = rl<sub>1</sub>/r(100-l<sub>1</sub>)</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">R/S = l<sub>1</sub>/(100-l<sub>1</sub>)</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">Where ‘r’ is the resistance of wire per unit length of meter bridge.</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">S = R (100-l<sub>1</sub>)/ l<sub>1</sub></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">Using this formula, we can find out the unknown resistance.</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"><b><u>POTENTIOMETER </u>:-</b> it is an instrument which is used to measure potential difference .</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"><b><u>PRINCIPLE OF POTENTIOMETER WIRE </u>:-</b> If a constant current is passing through the wire of uniform area of cross-section of potentiometer, then the potential drop across any portion of the wire is directly proportional to the length of that portion of the wire.</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">We know that,</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> V = IR</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"> But R = ρl/A</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">V =Iρl/A</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">Or V =kl</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">Where k = Iρ/A is called the potential gradient.</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">V</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;"><b><u>APPLICATION OF POTIOMETER WIRE </u>:-</b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="font-size: small;">1.<b><u>To find out ratio of emf of two cells</u></b>:- there are two cells having enf E<sub>1</sub> & E<sub>2</sub> connected as per circuit diagram. First we use the cell of emf E<sub>1</sub> & suppose by using this cell, the null point comes out at a length l<sub>1</sub> from end A & by using the second cell of<b> </b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;">emf E<sub>2</sub> suppose the balancing length is </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;">at length `l<sub>2</sub>’ from end A. </span></div><div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNwGcUv3ETzsdPW66GOxU5gJkNxszgVdpdqWS69sR1opxBQiwy0uVN73Dg27_UndQ4VGiV0IPHHD9JavEjVRm2f1NXpsB1qwfyDQVf783PPBCu_bIqgN6gqZV-WPJWBsUvJdRMW146pva1/s1600/New+Picture+%286%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="207" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNwGcUv3ETzsdPW66GOxU5gJkNxszgVdpdqWS69sR1opxBQiwy0uVN73Dg27_UndQ4VGiV0IPHHD9JavEjVRm2f1NXpsB1qwfyDQVf783PPBCu_bIqgN6gqZV-WPJWBsUvJdRMW146pva1/s320/New+Picture+%286%29.png" width="320" /></a></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> </span></div><div align="center" class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: center;"></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left; text-indent: -13.5pt;"><span style="font-size: small;"> Then E<sub>1</sub>=kl<sub>1</sub> &</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> E<sub>2 =</sub>kl<sub>2 </sub></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> Therefore <b>E<sub>1</sub>/ E<sub>2</sub>=l<sub>1</sub>/l<sub>2</sub></b></span> </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left; text-indent: -0.75in;"><br />
</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 13.5pt; text-align: left; text-indent: -13.5pt;"><span style="font-size: small;">2<b>. To find the internal resistance of cell:-</b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left; text-indent: -0.75in;"><span style="font-size: small;"> In the given circuit diagram , a cell of </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left; text-indent: -0.75in;"><span style="font-size: small;"> emf E is connected alongwith a key </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left; text-indent: -0.75in;"><span style="font-size: small;"> & resistance box. Suppose the internal </span></div><div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;"><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnEHcuxMAChGpOqSI6kPxE3-Vp-AO2SbAysmXgjOCMFrafBJbNe3rGwuyxKKkVfjA6ypz8SQm8FjuxK4mfYoVVR5WbyEZDs0DRF5p3rKLSqMNBf72j14Nwm4UyZjCr_E9wKgqs4ntsHdz6/s1600/New+Picture+%287%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="208" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnEHcuxMAChGpOqSI6kPxE3-Vp-AO2SbAysmXgjOCMFrafBJbNe3rGwuyxKKkVfjA6ypz8SQm8FjuxK4mfYoVVR5WbyEZDs0DRF5p3rKLSqMNBf72j14Nwm4UyZjCr_E9wKgqs4ntsHdz6/s320/New+Picture+%287%29.png" width="320" /></a></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left; text-indent: -0.75in;"><span style="font-size: small;"> </span></div><div align="center" class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: center; text-indent: -0.75in;"><span style="font-size: small;"><b></b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> resistance of the cell is `r’.</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.75in; text-align: left; text-indent: -0.75in;"><span style="font-size: small;"> </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.75in; text-align: left; text-indent: -0.75in;"><span style="font-size: small;"> let when the key K<sub>2</sub> is open , balance point isat length l<sub>1 </sub>then </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; margin-left: 0.75in; text-align: left; text-indent: -0.75in;"><span style="font-size: small;"> E=kl<sub>1 </sub> ………………………. (1)</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> Now when the key k<sub>2 </sub>is closed , suppose the Balance point is at length l<sub>2 </sub> then terminal potential difference of cell is </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> V=kl<sub>2</sub> ………………….. (2)</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> Therefore E/V=l<sub>1</sub>/l<sub>2</sub></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> But we have the relation </span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> r=R(E/V -1)</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> therefore <b>r=R(l<sub>1</sub>/l<sub>2</sub> -1)</b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> by knowing the length l<sub>1 </sub>& l<sub>2 </sub>, we can find out the value of internal resistance `r’</span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; text-align: left;"><span style="font-size: small;"> </span> </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"><span style="font-size: large;"><b>SOME IMPORTANT QUESTION:-</b></span></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">1. Derive relation between current & drift velocity (CBSE 2003) </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">2. Define term resistivity & conductivity & state their units.</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> (CBSE 2001-03)</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">3. Explain colour code for carbon resisters with illustration. </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">4. The variation of potential difference </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> V with length l in case of two potentiometer </div><div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxGoazdFJgxBfPFKKdCrTOMN7_EKUPLIU0_r-EjWb_DgakdTCPZQFf4I24gFTRYyuU2rN6RT6HDMIp1YHnyrIqnCWFFabsMfHVKJ4ju7O5sBO2uXyWHPBbC2IVU9TGonX7wRRztBNDUNT0/s1600/New+Picture+%288%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxGoazdFJgxBfPFKKdCrTOMN7_EKUPLIU0_r-EjWb_DgakdTCPZQFf4I24gFTRYyuU2rN6RT6HDMIp1YHnyrIqnCWFFabsMfHVKJ4ju7O5sBO2uXyWHPBbC2IVU9TGonX7wRRztBNDUNT0/s1600/New+Picture+%288%29.png" /></a></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> </div><div align="center" class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-align: center; text-indent: -0.75in;"></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> X & Y is as shown in fig. Which one of </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> these two will you prefer for comparing </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> emf ‘s of two cells & why? (CBSE 2006)</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">5. State Wheat stone bridge principle & deduce it using Kirchhoff’s laws. (CBSE 2002)</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">6. With a circuit diagram, explain how a meter bridge can be used to find the unknown resistance of a given wire. State the formula used. </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> (CBSE 2001)</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">7. State principle of Wheat stone bridge. Draw a circuit diagram used </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> to compare the emf of two cells. Write the formula used. How the </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> sensitivity of a potentiometer can be increased. (CBSE 2006)</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">8. Copper wire of resistance R<sub>0</sub> is stretched till its length is increase to</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> `n’ times of its original length. What is its new resistance.</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">9. A 10meter long wire AB of uniform area </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">of cross-section & 20Ω resistance is used as</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> a potentiometer wire. This wire is connected </div><div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNQfCO-tQnhCQ27p0y6EklXWHlG_8EKtEGrQATOhPl5rINpjcxp2CcBPpRWgDUBRkm7X5kdtsy0nCvOwqgnKesK4bcj_dqahkifVNiGagKPawv6b89CCPX537e0iQnXkdiQhqyHVyuQL8v/s1600/New+Picture+%25289%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNQfCO-tQnhCQ27p0y6EklXWHlG_8EKtEGrQATOhPl5rINpjcxp2CcBPpRWgDUBRkm7X5kdtsy0nCvOwqgnKesK4bcj_dqahkifVNiGagKPawv6b89CCPX537e0iQnXkdiQhqyHVyuQL8v/s320/New+Picture+%25289%2529.png" width="320" /></a></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"></div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">in series with a battery of 5V & a resistor of </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">480 Ω. A unknown emf is balanced at 600cm </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;">of the wire as shown in fig. Calculate-</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> 1-The potential gradient for the potentiometer wire.</div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> 2-The value of unknown emf </div><div class="MsoNormal" style="font-family: Arial,Helvetica,sans-serif; line-height: 150%; margin-left: 0.75in; text-indent: -0.75in;"> (CBSE 1998)</div></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0tag:blogger.com,1999:blog-4369263199692872808.post-75156929934939917282012-03-12T18:03:00.001-07:002012-03-12T18:04:47.915-07:00Rutherford Α Particle Scattering<div dir="ltr" style="text-align: left;" trbidi="on"><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlsIoqgE8KHVAmc0q2T64LoYEQ6MjkOqO-40FmBxQKuNANkk21fI8KAKPZ0EKHJjCWT26CrMFLYiRh5zX5s4jHi4SqNYGMjP6KvBBmbp-T8MEJ0n34rsUHcMZWY0brpIB7zs-FXpxUZ0V5/s1600/New+Picture.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlsIoqgE8KHVAmc0q2T64LoYEQ6MjkOqO-40FmBxQKuNANkk21fI8KAKPZ0EKHJjCWT26CrMFLYiRh5zX5s4jHi4SqNYGMjP6KvBBmbp-T8MEJ0n34rsUHcMZWY0brpIB7zs-FXpxUZ0V5/s1600/New+Picture.png" /></a></div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
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<div class="MsoNormal" style="margin-left: 45pt; text-indent: 27pt;">1<span style="font-family: "Arial","sans-serif";">.) Beam Of Α Particle Allowed Fall On A Thin Foil Of Gold.</span></div><div class="MsoNormal" style="margin-left: 45pt;"><br />
</div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-family: "Arial","sans-serif";">2. Scattered Α Particle Were Observed Through A Roatating Detector Consisting Of Zinc- Sulphide Screen.</span></div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-family: "Arial","sans-serif";">3.) Scattered Α Particle Strik The Zinc Sulphide Screen Produce Flashes;Ie Called “ Scientillations</span>”.</div><div class="MsoNormal" style="margin-left: 45pt;"><br />
</div><div class="MsoNormal" style="margin-left: 45pt;"><b>Observation</b></div><div class="MsoNormal" style="margin-left: 45pt;">A Graph Is Plotted Between The Sacttered Angle Θ And Number Of Α-Scattered Particle N(Θ) .. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdg2_T2QrMEcrjCMpm1h68yVAco1NZE3DPepVAEhEe7_LiANEhT7k9kYuTPFr0n9eEZbXm-3cwmQrxNztMw2qnDGkag7QSoNrOg80-8Hz6HuplR5m0CMGigjbVjDAnpwIbJdTpbYQVxLe_/s1600/New+Picture+%281%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdg2_T2QrMEcrjCMpm1h68yVAco1NZE3DPepVAEhEe7_LiANEhT7k9kYuTPFr0n9eEZbXm-3cwmQrxNztMw2qnDGkag7QSoNrOg80-8Hz6HuplR5m0CMGigjbVjDAnpwIbJdTpbYQVxLe_/s1600/New+Picture+%281%29.png" /></a></div><div class="MsoNormal" style="margin-left: 45pt;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="margin-left: 45pt;">From This Graph We Observed That --</div><div class="MsoNormal" style="margin-left: 45pt;"> </div><div class="MsoNormal" style="margin-left: 45pt; text-indent: -0.25in;">1.)<span style="font: 7pt "Times New Roman";"> </span>Most Of The Α-Particle Pass Through The Foil And Suffer Small Scattering Angle .</div><div class="MsoNormal" style="margin-left: 45pt; text-indent: -0.25in;">2.)<span style="font: 7pt "Times New Roman";"> </span>The Α-Particle Defelected Backwards And Experience A Laeg Repulsive Force When It Goes Very Close To Central Part Of Atom Where The Whole Mass Of Atom And Positive Charge Is Concentrated.</div><div class="MsoNormal" style="margin-left: 45pt; text-indent: -0.25in;">3.)<span style="font: 7pt "Times New Roman";"> </span>The Central Part Of Atom Is Called “Nucleus”.</div><div class="MsoNormal" style="margin-left: 45pt; text-indent: -0.25in;">4.)<span style="font: 7pt "Times New Roman";"> </span>Size Of Nucleus Is About 10<sup>-</sup>¹<sup>5</sup> M To 10<sup>-14</sup> M.</div><div class="MsoNormal" style="margin-left: 45pt; text-indent: -0.25in;">5.)<span style="font: 7pt "Times New Roman";"> </span>Size Of Atom Is 10<sup>-10 </sup>M.</div><div class="MsoNormal" style="margin-left: 45pt; text-indent: -0.25in;"><b>6.)<span style="font: 7pt "Times New Roman";"> </span></b>The Maginitued Of Force Is <b>F=1/4πє<sub>0</sub>*(Ze)2e/R<sup>2</sup></b></div><div class="MsoNormal" style="margin-left: 45pt;"><br />
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</div><div class="MsoNormal" style="margin-left: 0.25in;"><u>Bhor`S Model Of Hydrogen Atom Postulates </u></div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;">1.) An Electronin Atom Revolve In A Certain Stable Orbits With Out The Emission Of Radiant Energy .This Certain Stable Orbits Are Called Stationary Orbit .</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;">2.) The Electron Revolves Arround The Nucleus Only In Those Orbits For Which The Angular Momentum Is Integral Multiple Of h /2π;</div><div class="MsoNormal" style="margin-left: 0.25in;"> i.e.<b>L=nh/2π</b></div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 1.25in; text-indent: 0.25in;"> L=mvr </div><div class="MsoNormal" style="margin-left: 0.25in;"> L<sub>n </sub> =mv<sub>n</sub>r<sub>n</sub></div><div class="MsoNormal" style="margin-left: 0.25in;"> Mv<sub>n</sub>r<sub>n</sub>=nh/2π WHERE r<sub>n</sub>= RADIUS OF n<sup>th</sup> ORBIT. </div><div class="MsoNormal" style="margin-left: 0.25in;"> V<sub>n</sub>=SPEED OF ELECTRON.</div><div class="MsoNormal" style="margin-left: 0.25in;">3.)When An Electron Jump From Higher Energy Level To Another Energy Level Or Vice-Versa A Photon Is Emmited Having Energy Equal To Energy Different Between Initial And Final States .</div><div class="MsoNormal" style="margin-left: 1.75in;">i.e. hυ=E<sub>i</sub>-E<sub>f</sub></div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 2.5in; text-indent: 0.5in;">E<sub>i</sub>=ENERGY OF INITIAL STATE.</div><div class="MsoNormal"> E<sub>f</sub>=ENERGY OF FINAL STATE.</div><div class="MsoNormal"><br />
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</div><div class="MsoNormal"><b> TOTAL ENERGY OF THE ELECTRON IN STATIONARY STATE OF HYDROGEN ATOM IS GIVEN BY </b></div><div class="MsoNormal"> </div><div class="MsoNormal" style="margin-left: 1.5in; text-indent: 0.5in;"> E<sub>n</sub>=-13.6/n<sup>2</sup>*ev</div><div class="MsoNormal" style="margin-left: 45pt;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal"><b>ENERGY LEVEL DIAGRAM FOR HYDROGEN ATOM<sub> </sub></b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgksQ-0bHQi2BpghWgUuNNOGxhfL1Olfe7zNooLpxJlUzcvDyCMAnTi1D0EioQxTPA9vV-2Bi7woDuIdBf1VVGhy2Ax4U0wlMxWI4AcMzZ-OZTrlh75HVdYuLrm4HNp2ubRj2kO_EwNMtZN/s1600/New+Picture+%282%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgksQ-0bHQi2BpghWgUuNNOGxhfL1Olfe7zNooLpxJlUzcvDyCMAnTi1D0EioQxTPA9vV-2Bi7woDuIdBf1VVGhy2Ax4U0wlMxWI4AcMzZ-OZTrlh75HVdYuLrm4HNp2ubRj2kO_EwNMtZN/s1600/New+Picture+%282%29.png" /></a></div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">The Energy Of State(N=1) E<sub>1</sub>=-13.6ev Is Called Ground State.</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">The Minimum Energy Required To Free A Electron Form The Ground State Of Hydrogen Atom Is 13.6ev.It Is Called <b><u>Ionisation Energy</u></b> Of Hydrogen Atom.</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">When An Electron Jump From n=2 TO n=1</div><div class="MsoNormal" style="line-height: 150%; margin-left: 1.75in; text-indent: 0.25in;">E<sub>2</sub>-E<sub>1</sub>=-3.40ev-(-13.6ev)=10.2ev .</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">As The Excitation State Of Hydrogen Atom Increases(I.E.N Increases)The Value Of Minimum Energy Required To Free The Electron From excited Atom Decreases.</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"> i.e E<sub>3</sub>-E<sub>1</sub>=-1.51ev-(-13.6ev)=12.9ev.</div><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"></span> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
<div class="MsoNormal" style="margin-left: 0.25in;"><b>SPECTRA LINES OF HYDROGEN ATOM</b></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLZlbWtcVll4W3lXeRtlSlSjydpRMuMXy6dFLQLm2RMKk_vh43vBkEdrRytG6s-GsHty0RrONz3oGuu_5YyM3-oFKpgPsfQQu0UKXUPxer5a_o8K2tIQB5CHasqzA_yhN3A9tbywBBbi1s/s1600/New+Picture+%286%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLZlbWtcVll4W3lXeRtlSlSjydpRMuMXy6dFLQLm2RMKk_vh43vBkEdrRytG6s-GsHty0RrONz3oGuu_5YyM3-oFKpgPsfQQu0UKXUPxer5a_o8K2tIQB5CHasqzA_yhN3A9tbywBBbi1s/s320/New+Picture+%286%29.png" width="298" /></a></div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <br />
<div class="MsoNormal" style="margin-left: 0.25in;">WAVE NUMBER ὺ OF THE EMITEED PHOTONS IS GIVEN BY </div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: 0.25in;"> ὺ=R[1/n<sub>f</sub><sup>2</sup>-1/n<sub>i</sub><sup>2</sup>] WHERE n<sub>i</sub>=QUANTUM NUMBER OF HIGHER ENERGY STATE </div><div class="MsoNormal" style="margin-left: 0.25in;"> n<sub>f</sub>=QUANTUM NUMBER OF LOWER ENERGY STATE</div><div class="MsoNormal" style="margin-left: 0.25in;"> ὺ=WAVE NUMBER </div><div class="MsoNormal" style="margin-left: 0.25in;"> R=RYDBERG CONSTANT</div><div class="MsoNormal" style="margin-left: 0.25in;">1. <b>LYMAN SERIES</b>:WHEN ELECTRON JUMP FROM ANY HIGHER ENERGY LAVEL TO FIRST LEVEL.</div><div class="MsoNormal" style="margin-left: 0.25in;"> ὺ=R[1/1<sup>2</sup>-1/n<sub>i</sub><sup>2</sup>],</div><div class="MsoNormal" style="margin-left: 1.75in; text-indent: 0.25in;">WHERE n<sub>i</sub>=2,3,4,…..</div><div class="MsoNormal" style="margin-left: 0.25in;"> THIS SERIES LIES IN ULTRA VIOLET REGION.</div><div class="MsoNormal" style="margin-left: 0.25in;">2.<b>BALMER SERIES</b>:</div><div class="MsoNormal"> ὺ=R[1/2<sup>2</sup>-1/n<sub>i</sub><sup>2</sup>],</div><div class="MsoNormal" style="margin-left: 2in;">WHERE n<sub>i</sub>=3,4,5…</div><div class="MsoNormal" style="margin-left: 0.25in;"> THIS SERIES LIES IN THE VISIBLE REGION.</div><div class="MsoNormal" style="margin-left: 0.25in;">3<b>.PASCHEN SERIES</b>:</div><div class="MsoNormal"> ὺ=R[1/3<sup>2</sup>-1/n<sub>i</sub><sup>2</sup>],</div><div class="MsoNormal" style="margin-left: 1.5in; text-indent: 0.5in;">WHERE n<sub>i</sub>=4,5,6…</div><div class="MsoNormal" style="margin-left: 0.25in;"> THIS SERIES LIES IN THE INFRA RED REGION.</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
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</div><div class="MsoNormal" style="margin-left: 0.25in;">4<b>.BRACKTT SERIES</b>:</div><div class="MsoNormal"> ὺ=R[1/4<sup>2</sup>-1/n<sub>i</sub><sup>2</sup>],</div><div class="MsoNormal" style="margin-left: 2in; text-indent: 0.5in;">WHERE n<sub>i</sub>=5,6,7…</div><div class="MsoNormal" style="margin-left: 0.25in;"> THIS SERIES LIES IN THE INFRA RED REGION</div><div class="MsoNormal" style="margin-left: 0.25in;">5.<b>PFUND SERIES</b>:</div><div class="MsoNormal"> ὺ=R[1/5<sup>2</sup>-1/n<sub>i</sub><sup>2</sup>],</div><div class="MsoNormal" style="margin-left: 2in;"> WHERE n<sub>i</sub>=6,7,8…</div><div class="MsoNormal" style="margin-left: 0.25in;"> THIS SERIES LIES IN THE INFRA RED REGION</div><div class="MsoNormal" style="margin-left: 0.25in;">NUCLEI</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;">SIZE OF NUCLEUS:SIZE OF NUCLEUS IS DIRECTLY PROPORTIONAL TO ITS MASS NUMBER.</div><div class="MsoNormal"> 4/3Π R<sup>3 </sup>α A</div><div class="MsoNormal" style="text-align: justify;"> =>R<sup>3</sup>αA </div><div class="MsoNormal"> =>R αA<sup>1/3 </sup></div><div class="MsoNormal"> =>R =R<sub>0</sub>A<sup>1/3</sup></div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;">(R=RADIUS OF NUCLEUS , R<sub>0</sub> IS<sub> </sub>CONSTANT AND ITS VALUE IS 1.1*10<sup>-15</sup>m.)</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;">ISOTOPES:ATOM HAVING DIFFERENT MASS NUMBER(A) AND HAVING SAME ATOMIC NUMBER(Z)</div><div class="MsoNormal" style="margin-left: 0.25in;"> E.g. <sub>92</sub>U<sup>235</sup>,<sub> 92</sub>U<sup>238</sup></div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;">ISOBARS:ATOMS HAVING SAME MASS NUMBER(A)BUT DIFFERENT ATOMIC NUMBER (Z)</div><div class="MsoNormal" style="margin-left: 0.25in;"> E.g. <sub>24</sub>Cr<sup>54</sup> <sub>26</sub>Fe<sup>54</sup></div><div class="MsoNormal" style="margin-left: 0.25in;">ISOTONS:NUCLEI COANTAINING SAME NUMBER OF NEUTRONS ARE CALLED ISOTONS </div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;"> E.g.<sub>17</sub>Cl<sup>37</sup>,<sub> 19</sub>K<sup>39</sup></div><div class="MsoNormal" style="margin-left: 0.25in;">ATOMIC MASS UNIT:ONE u IS EQUAL TO 1/12<sup>th</sup> OF THE MASS OF AN ATOM OF <sub>6</sub>C<sup>12</sup> ISOTOPE OF CARBON.</div><div class="MsoNormal" style="margin-left: 0.25in;"> <b>1u EQUIVALENT TO 931.5 mev </b></div><div class="MsoNormal" style="margin-left: 0.25in;">MASS DEFECT:</div><div class="MsoNormal" style="margin-left: 0.25in;">DIFFERENCE BETWEEN THE SUM OF MASSES OF PROTONS AND NEUTRON AND ACTUAL MASS OF NUCLES IS CALLED MASS DEFECT.IT IS DENOTED BY ∆M.</div><br />
<div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;"><b>BINDING ENERGY</b>:</div><div class="MsoNormal" style="margin-left: 0.25in;">IF A CERTAIN NUMBER OF NEUTRONS AND PROTONS ARE BROUGHT TOGETHER TO FORM A NUCLEUS,AS ENERGY E<sub>b</sub> WILL REALSE IN THIS PROCESS.THIS ENERGY E<sub>b</sub> IS CALLED THE BINDING ENERGY.</div><div class="MsoNormal" style="margin-left: 0.25in;"> B.E. = ∆mc<sup>2</sup></div><div class="MsoNormal" style="margin-left: 0.25in;"> ∆M =Z<sub>mp</sub>+(A-Z)m<sub>n</sub>-M<sub>N</sub>(ZX<sup>A</sup>)</div><div class="MsoNormal" style="margin-left: 0.25in;"> Z<sub>mp </sub>=MASS OF PROTONS. <sub> </sub></div><div class="MsoNormal" style="margin-left: 0.25in;"> (A-Z)m<sub>n</sub>=MASS OF NEUTRON.</div><div class="MsoNormal" style="margin-left: 0.25in;"> M<sub>N</sub>(ZX<sup>A</sup>)=MASS OF NUCLEUS.</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;">B.E.=[ Z<sub>mp</sub>+(A-Z)m<sub>n</sub>+ Z<sub>me</sub>-M<sub>N</sub>(ZX<sup>A</sup>)-m<sub>e</sub>]C<sup>2 </sup> ( 931.5Mev)</div><div class="MsoNormal" style="margin-left: 0.25in;">B.E.=[Z(m<sub>p</sub>+m<sub>e</sub>)+ (A-Z)m<sub>n</sub>-{m<sub>n</sub>(ZX<sup>A</sup>)+ m<sub>e</sub>}] C<sup>2 </sup>(<sup> </sup>931.5Mev)</div><div class="MsoNormal" style="margin-left: 0.25in;">B.E.=[Zm<sub>H</sub>+(A-Z)m<sub>n</sub> -m(ZX<sup>A</sup>)] C<sup>2 </sup>(<sup> </sup>931.5Mev)</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;">m<sub>H</sub>=MASS OF HYDROGEN ATOM.</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;"><b>B.E. PER NUCLEOUS= TOTAL B.E./A</b></div><br />
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<div class="MsoNormal" style="margin-left: 0.25in;"><b>GRAPH BETWEEN BINDING ENERGY PER NUCLEOUS E<sub>bn </sub>VERSUS THE MASS NUMBER A</b></div><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"></span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOhowIVWerT7dEOyJH3pUsu-nZp-cc_N8YlPXNIzJRE-Y6IpDn1Z-is4i98Cg3Wicr0CZxiGLqU_nBi82WA7BqArvSS5kTzrStEXhcllWifo8DCMRLdVGfgcttF5msZVV3mDH1zLyM-mYc/s1600/New+Picture+%284%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOhowIVWerT7dEOyJH3pUsu-nZp-cc_N8YlPXNIzJRE-Y6IpDn1Z-is4i98Cg3Wicr0CZxiGLqU_nBi82WA7BqArvSS5kTzrStEXhcllWifo8DCMRLdVGfgcttF5msZVV3mDH1zLyM-mYc/s1600/New+Picture+%284%29.png" /></a></div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <br />
<div class="MsoNormal" style="margin-left: 0.25in;">B.E./NUCLIOUS WITH MASS NUMBER A REVEALS THAT-</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">1.LIGHT NUCLI LIKE <sub>1</sub>H<sup>1</sup>,<sub> 1</sub>H<sup>2</sup>,<sub> 1</sub>H<sup>3 </sup>HAVE SMALL VALUE OF B.E./A .</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in; text-align: justify;">2.FOR MASS NUMBER RANGING FROM 2 TO 20 HAVE VERY SHARP PEAKS CORRESPONDING TO NUCLIE HAVING MASS NUMBER IN MULTIPLES OF FOUR .</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">E.g. <b><sub>2</sub>He<sup>4</sup>,<sub>4</sub>Be<sup>8</sup>,<sub>6</sub>C<sup>12</sup>,<sub>8</sub>O<sup>16</sup>,<sub>10</sub>Ne<sup>20</sup></b></div><div class="MsoNormal" style="line-height: 150%; margin-left: 24.75pt;">PEAKS INDICATE THAT THESE NUCLIE ARE MORE STABLE THAN THE THE NUCLIE IN THE NEIGHBOURHOOD.</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">3. FOR MASS NUMBERS RANGUNG FROM 30 TO 120B.E.CURVE HAS A BROAD MAXIMUM.AVERAGE BE/A CORRESPONDING TO THIS RANG IS 8.5 Mev </div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">PEAK VALUE IS 8.8Mev /A (<sub>26</sub>Fe<sup>56</sup>)</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">ELEMENTS BELONGED TO THIN RANG ARE HIGHLY STABLE AND NON RADIOACTIVE.</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">4.AFTER A=120.B.E/A DECREASES GRADUALLY TO 7.6Mev/A (<sub>92</sub>U<sup>238</sup>).THUS HEAVY NUCLIE ARE LESS STABLE.</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;"><b>STABILITY OF A NUCLEUS DEPEND UPON ----</b></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">1.High Valu Of B.E/A.</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">2.Even-Even Nucleus(Even Z And Even A).It Is Found To Be More Stable,Even If It Has Comparatively Low Value Of B.E/A. An Even –Odd Nucleus Or Odd Even Nucleus Is Lesser Stable And Odd –Odd Nucleus Is Least Stable.</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">3. Nuclei Having Higher Or Lower Value Of Neutron To Proton Ratio Than The Stable Nuclie Are Also Un Stable.</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"><b>MAIN FEATURE OF THE GRAPH B.E/A VERSUS A</b></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">1. The Binding Energy Per Nucleos E<sub>bn</sub> Is Practically Constant.The Curv Has A Maximum Of About 8.75mevfor A=56 And Has A Value Of 7.6 Mev For A=238.</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">2. E<sub>bn </sub>Is Lower For Both Light Nuclei A<30 And Havy Nuclei A>170.</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"><b>FOLLOWING RESULTS FROM THESE TWO OBSERVATION IS UNDER –</b></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in; text-align: justify;">1.The Force Is Attractive And Sufficiently Strong To Produce a Binding Of A Few Mev Per Nucleon.</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">2.The Binding Energy In The Range 3o<A<17o Is A </div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">3.A Very Heavy Nucleus Has Lower Binding Energy Per Nucleon.This Impalies Energy Would Be Realse In This Process Of Fission..</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">4.The Binding Energy Per Nucleous Of Fused Havier Nuclei Is More Than The Binding Energy Per Nucleon, Of The Light Nuclei.This Implies That Energy Would Be Released In The Process Of Fusion.</div><div class="MsoNormal" style="margin-left: 0.25in;"><b><i><span style="font-family: "Arial Black","sans-serif";"> </span></i></b></div><div class="MsoNormal" style="margin-left: 0.25in;"><b><i><span style="font-family: "Arial Black","sans-serif";"> </span></i></b><b><u><span style="font-family: "Arial Black","sans-serif";">RADIOACTIVITY </span></u></b><b><i><span style="font-family: "Arial Black","sans-serif";"></span></i></b></div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;">Radio Activity: Radioactivity Is Phenomenon In Which A Heavy Nucleus Distintegrate Itself .The Element Exhibiting This Property Is Called Radioactive Element . Thair Nuclei Are Unstable Nuclei E.G. Radium , Thorium, Actinium , Polarium.</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;">Redioactive Decay:Three Type Of Radioactive Decay Occur In Nature </div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">1.α-DECAY –α-DECAY IN WHICH HELIUM NUCLUES 2He<sup>4 </sup>IS EMITED </div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">2. β-DECAY –IN β – DECAY ELECTRON OR POSITORN ARE EMITTED .</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;"><sup>3. γ-DECAY – </sup>IN WHICH HIGH ENERGY PHOTON ARE EMITTED .</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in;"><b>LAW OF REDIOACTIVE DECAY </b></div><div class="MsoNormal" style="margin-left: 0.5in; text-indent: -0.25in;"><span style="font-size: 16pt;">-<span style="font: 7pt "Times New Roman";"> </span></span>When A Radioactive Substances Under Goes Α; Β And Γ Decay It Is Observed That Number Of Nucliei Undergoing The Decay Per Unit Time Is Proportional To Total Number Of Nuclei Is Present . </div><div class="MsoNormal" style="margin-left: 0.5in; text-indent: -0.25in;"><span style="font-size: 16pt;">-<span style="font: 7pt "Times New Roman";"> </span></span>In Sample </div><div class="MsoNormal" style="margin-left: 0.25in;">. If N Is Number Of Nuclei In The Sample And Δn Under Goes Decay In Time Δt,Then </div><div class="MsoNormal" style="margin-left: 0.25in;"> ΔN/Δt α -N</div><div class="MsoNormal" style="margin-left: 0.25in;"> </div><div class="MsoNormal" style="margin-left: 0.25in;"> =>dN/dt α -N </div><div class="MsoNormal" style="margin-left: 0.25in;"> . – =>dN/dt=-λN </div><div class="MsoNormal" style="margin-left: 0.25in;">WHERE λ IS CALLED DECAY CONSTANT OR DISINTERGRATION CONSTANT</div><div class="MsoNormal" style="margin-left: 0.25in;">HERE -ve SIGN SHOWS THAT ONE OF ORIGINAL NUCLEI,ΔN HAVE DECAYED. </div><div class="MsoNormal" style="margin-left: 0.25in;"> =>dN/N=-λdt</div><div class="MsoNormal" style="margin-left: 0.25in;"> <sub>No</sub>∫<sup>N</sup> dN/N=-λ ∫<sub>0</sub><sup>t</sup>dt</div><div class="MsoNormal" style="margin-left: 1.25in; text-indent: 0.25in;">=> <sub>No</sub>∫<sup>N</sup>log<sub>e</sub> N= -λ[t]<sub>o</sub><sup>t </sup>= -λt</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 1in; text-indent: 0.5in;">=> log<sub>e</sub>N- log<sub>e</sub>N<sub>0 </sub>= - λt</div><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 1in; text-indent: 0.5in;">log<sub>e</sub>N/N<sub>0</sub>=-λt</div><div class="MsoNormal" style="margin-left: 0.25in;"><sup> </sup></div><div class="MsoNormal" style="margin-left: 0.25in;"><sup> </sup>N/N<sub>0</sub>=e<sup>-λt</sup></div><div class="MsoNormal" style="margin-left: 0.25in;"> <table align="left" cellpadding="0" cellspacing="0"><tbody>
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</td> <td bgcolor="white" height="54" style="background: none repeat scroll 0% 0% white; border: 0.75pt solid black; vertical-align: top;" width="174"><span style="left: 0pt; position: absolute; z-index: 251658240;"> <table cellpadding="0" cellspacing="0"><tbody>
<tr> <td><div class="shape" style="padding: 4.35pt 7.95pt;"><div class="MsoNormal"> N= N<sub>0 </sub>e<sup>-λt</sup></div></div></td> </tr>
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</tbody></table><sup> </sup></div><br clear="ALL" /> <div class="MsoNormal"> </div><div class="MsoNormal"> </div><div class="MsoNormal"><br />
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</div><div class="MsoNormal"> 4. <b><u>DISINTEGRATE CONSTANT</u></b></div><div class="MsoNormal"> N=N<sub>0</sub>e<sup>-λt</sup> ,IF t=1/λ</div><div class="MsoNormal"> N=N<sub>0</sub>e<sup>-λ*1/λ</sup></div><div class="MsoNormal"> N=N<sub>0</sub>e<sup>-1 </sup>= N=N<sub>0</sub>/e</div><div class="MsoNormal"> λ=1/t</div><div class="MsoNormal"><br />
</div><div class="MsoNormal">5<b><u>. HALF LIFE AND MEAN LIFE:</u></b></div><div class="MsoNormal" style="margin-left: 0.5in;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in;">Half Life:Half Life Is The Time In Which One-Half Of The Radioactive Substance Is Dis Intigrated.</div><div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">IT IS DENOTED BY T<sub>1/2</sub></div><div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;"> t= T<sub>1/2 ;</sub> N= N<sub>0</sub>/2</div><div class="MsoNormal" style="line-height: 150%;"> ·.· N=N<sub>0</sub>e<sup>-λt</sup></div><div class="MsoNormal" style="line-height: 150%;"> => N<sub>0</sub>/2=N<sub>0</sub>e<sup>-λ*1/λ</sup>= N<sub>0 </sub>e<sup>-</sup><sub> </sub><sup>λT½ </sup>·.·t=T<sub>½</sub></div><div class="MsoNormal" style="line-height: 150%;"> =>1/2= e<sup>- λT½ </sup>=1/ e<sup>λT½</sup></div><div class="MsoNormal" style="line-height: 150%;"> 2= e<sup>λT½</sup></div><div class="MsoNormal" style="line-height: 150%;"> TAKING log ON BOTH SIDE </div><div class="MsoNormal" style="line-height: 150%;"> log<sub>e</sub>2 = log<sub>e</sub>e<sup>λT½</sup></div><div class="MsoNormal" style="line-height: 150%;"> =λT<sup>½</sup> log<sub>e</sub>e</div><div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;"> 3.303* log<sub>e</sub>10<sup>2</sup>=λT<sup>½</sup></div><div class="MsoNormal" style="line-height: 150%;"> λT<sup>½ </sup>=3.303*0.3010=0.693</div><div class="MsoNormal" style="line-height: 150%;"> <b>T<sup>½ </sup>= 0.693/λ</b></div><div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;"> IMPORTANT</div><div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;"> t= <b>T<sup>½ </sup></b> =T </div><div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;"> N= N<sub>0</sub>/2</div><div class="MsoNormal" style="line-height: 150%;"> IN ANOTHER HALF LIFE (i.e.AFTER 2 HALF LIFE t=2T)</div><div class="MsoNormal" style="line-height: 150%;"> N=1/2*N<sub>0</sub>/2 = N<sub>0</sub>/4 = N<sub>0 </sub>(1/2)<sup>2</sup></div><div class="MsoNormal" style="line-height: 150%;"> AFTER ANOTHER HALF LIFE(i.e.AFTER 3 HALF LIFE t=3T)</div><div class="MsoNormal" style="line-height: 150%;"> N= N<sub>0</sub>/4*1/2 = N<sub>0</sub>/8= N<sub>0</sub>(1/2)<sup>3 </sup> AND SO ON </div><div class="MsoNormal" style="line-height: 150%;"> </div><div class="MsoNormal" style="line-height: 150%;"> FOR n HALF LIFE </div><div class="MsoNormal" style="line-height: 150%;"><br />
</div><div class="MsoNormal" style="line-height: 150%;"> ·.· N = N<sub>0 </sub>(1/2)<sup>n</sup> </div><div class="MsoNormal" style="line-height: 150%;"> ·.·t=nT =>n=t/T</div><div class="MsoNormal"> <table align="left" cellpadding="0" cellspacing="0"><tbody>
<tr> <td height="3" width="83"><br />
</td> </tr>
<tr> <td><br />
</td> <td bgcolor="white" height="46" style="background: none repeat scroll 0% 0% white; border: 0.75pt solid black; vertical-align: top;" width="389"><span style="position: absolute; z-index: 251657216;"> <table cellpadding="0" cellspacing="0"><tbody>
<tr> <td><div class="shape" style="padding: 4.35pt 7.95pt;"><div class="MsoNormal"><b><i><span style="font-family: "Arial Black","sans-serif";"> </span></i></b><span style="font-family: "Arial Black","sans-serif";">N=N<sub>0</sub>(1/2)<sup>n</sup>= N<sub>0</sub>(1/2)<sup>t/T</sup></span></div></div></td> </tr>
</tbody></table></span> </td> </tr>
</tbody></table> </div><br clear="ALL" /> <div class="MsoNormal"> =></div><div class="MsoNormal"><br />
</div><div class="MsoNormal"> T=TOTAL TIME OF n HALF LIFE </div><div class="MsoNormal"> n=n NUMBER OF HALF LIFE</div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><b> t = total time of n half life </b></div><div class="MsoNormal"><b> n = no. of half life </b></div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><b>Average life or mean life: </b>AVERAGE LIFE OF A RADIOACTIVE ELEMENT IS RECIPROCAL OF THE DECAY CONSTANT OF THE ELEMENT</div><div class="MsoNormal"><b> i.e. τ = 1/ λ </b></div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><b><i>τ =</i></b> SYMBOL OF AVERAGE LIFE OR MEAN LIFE.</div><div class="MsoNormal"> =><b><i> τ= 1/0.693*T ,</i></b> ·.·λ=0.693/T</div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><b>=> τ=T/0.693 , T=HALF LIFE </b></div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><b>=> τ=1.44T , λ=DECAY CONSTANT.</b></div><div class="MsoNormal"><br />
</div><div class="MsoNormal">THUS AVERAGE LIFE OF A RADIO SUBSTANCE IS 1.44 TIMES THE HALF LIFE OF ELEMENT.</div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><b>RADIO-ACTIVE DECAY </b></div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><b>ALPHA DECAY</b>-</div><div class="MsoNormal" style="text-align: justify;"> IT IS THE PHENOMENON OF EMISSION OF AN <b>α PARTICLE </b> FROM A radioactive NUCLEUS. When a nucleus EMITS AN <b>α –PARTICLE</b> , ITS MASS NUMBER DECREASE BY 4 AND CHARGE NUMBER (ATOMIC NUMBER ) DECREASE BY 2.</div><div class="MsoNormal"> ZX<sup>A</sup>→(Z-2)Y<sup>(A-4)</sup>+<sub>2</sub>He<sup>4</sup>+Q</div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><sub>92</sub>U<sup>238</sup>→<sub>90</sub>Th<sup>234</sup>+<sub>2</sub>He<sup>4</sup>+Q</div><div class="MsoNormal"><br />
</div><div class="MsoNormal">X=u,Y=Th.X=PARENT ELECTRON,Y=DAUGHTER ELECTRON.</div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><span style="position: relative; top: 5pt;"><img height="21" src="file:///C:/DOCUME%7E1/AMITGA%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif" width="16" /></span><b>-DECAY</b>:</div><div class="MsoNormal"> IT IS THE PHENOMENON OF EMISSION OF AN ELECTRON FROM A RADIOACTIVE NUCLEUS .</div><div class="MsoNormal"> </div><div class="MsoNormal"> ZX<sup>A</sup>→(Z+1)Y<sup>A </sup>+ <sub>-1</sub>e<sup>0</sup>+ Q</div><div class="MsoNormal"> IN <span style="position: relative; top: 5pt;"><img height="21" src="file:///C:/DOCUME%7E1/AMITGA%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif" width="16" /></span>-DECAY:- A NUCLEUS SPONTANOUSLY EMITS AN <b>ELECTRON </b>(β<sup>-</sup>DECAY)OR A POSISOTRON (β<sup>+</sup>DECAY)</div><div class="MsoNormal"><br />
</div><div class="MsoNormal"> EX.OF β<sup>- </sup>DECAY -</div><div class="MsoNormal"><sub> 15</sub>P<sup>32</sup>→<sub>16</sub>S<sup>32</sup>+<sub>-1</sub>e<sup>0</sup>+ύ <sub>-1</sub>e<sup>0</sup>=ELECTRON , ύ=ANTI NUTRINO</div><div class="MsoNormal"><sub> </sub>EX.OF β<sup>+ </sup>DECAY<sub> </sub></div><div class="MsoNormal"><sub> 11</sub>Na<sup>22</sup>→<sub>10</sub>Ne<sup>22</sup>+<sub>+1</sub>e<sup>0</sup>+ύ <sub>+1</sub>e<sup>0</sup>=POSITRON , ύ=NUTRINO</div><div class="MsoNormal"><br />
</div><div class="MsoNormal">DURING β<sup>- </sup>DECAY n/P RATIO DECREASES </div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><b><span style="font-size: 16pt;">γ</span>-DECAY</b>: PHENEMENON OF EMISSION OF γ RAYS PHOTON FROM A RADIOACTIVE NUCLEUS IS CALLED γ-DECAY</div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFX9Wp7odQXLnVuCXpDWeifIbeGxPSKUgW5uJS0LhfOlcfePFIVCWw9Kn9H-c-1F3eHhWFUTGs9YpofWsFvbcSlWe_De4jMA-tNSXcLdzK9yUD0oTEKK5es2iRzGha2heQBdueta-wiKsm/s1600/New+Picture+%285%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="206" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFX9Wp7odQXLnVuCXpDWeifIbeGxPSKUgW5uJS0LhfOlcfePFIVCWw9Kn9H-c-1F3eHhWFUTGs9YpofWsFvbcSlWe_De4jMA-tNSXcLdzK9yUD0oTEKK5es2iRzGha2heQBdueta-wiKsm/s320/New+Picture+%285%29.png" width="320" /></a></div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <div class="MsoNormal" style="line-height: 150%;">β<sup>-</sup>DECAY OF <sub>27</sub>Co<sup>60</sup> NUCLEUS FOLLOWED BY EMISSION OF TWO γ-RAYS FROM DEEXCITATION OF THE DAUGHTER NUCLEUS<sub> 28</sub>Ni<sup>60</sup></div><div class="MsoNormal" style="line-height: 150%;"><br />
</div><div class="MsoNormal" style="line-height: 150%;"><br />
</div><div class="MsoNormal" style="line-height: 150%;"><br />
</div><div class="MsoNormal" style="line-height: 150%;"><br />
</div><div class="MsoNormal" style="line-height: 150%;"><br />
</div><div class="MsoNormal" style="line-height: 150%;"><br />
</div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><div class="MsoNormal"><b><u>NUMERICALS</u></b></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">Q1. THE VALUE OF GROUND STATE ENERGY OF HYDROGEN ATOM IS -13·6ev</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">(a)<span style="font: 7pt "Times New Roman";"> </span>WHAT DOES THE NEGATIVE SIGN SIGNIFY?</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">(b)<span style="font: 7pt "Times New Roman";"> </span>HOW MUCH THE ENERGY IS REQUIRED TO TAKE AN ELECTRON IN</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">THIS ATOM FROM IN IHE GROUND STATE TO THE FIRST EXITED STATE ?</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">Q2. TWO NUCLEI HAVE MASS NUMBER IN THE RATIO1:2,WHATE IS THE RATIO OF THEIR NUCLEAR RADII?</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">Q3 COMPARE THE RADII OF TWO NUCLEI WITH MASS NUMBER 1 AND 27 RESPECTIVELY?</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">Q4 THE HALF LIFE OF A RADIOACTIVE SUBSTANCE IS 30 sec CALCULATE </div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;"> 1.) THE DECAY CONSTANT </div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;"> 2.) TIME TAKEN FOR THR SAMPLE TO DECAY 3/4<sup>th</sup>OF ITS INITIAL VALUE?</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">Q5 THE SEQUENCE OF THE STEPWISE DECAY OF RADIOACTIVE NUCLEUS IS </div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;"> D-----<sup>ά</sup>--------> D<sub>1</sub>------ β -------> D<sub>2</sub>-----<sup>ά</sup>-------->D<sub>3</sub>-----<sup>ά</sup>-------->D<sub>4</sub></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;"> IF NUCLEON NUMBER & ATOMIC NUMBER FOR D<sub>2</sub> 176 & 171 THEN WRITE CORRESPONDING VALUE OF D<sub>3 & </sub>D<sub>4 </sub></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">Q6 Draw The Graph Showing The Varition Of Binding Energy Per Nucleous With Mass Number.Give The Reason For The Decreases Of Binding Energy Per Nucleus For Nuclei With High Mass Number?</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">Q7 Define Half Life And Disintegration Constant.Derive The Relation Between The </div><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: center; text-indent: -0.5in;">i.e. T<sup>1/2</sup>=0.693/λ</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">Q8 THE ACTIVITY OF A RADIOACTIVE ELEMENT DROP TO 1/6<sup>th</sup> OF ITS INITIAL VALUE IN 32 YEARS.FIND HALF LIFE AND MEAN LIFE OF THE SAMPLE .</div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;">Q9 THE ENERGY LEVEL OF AN ATOM ARE AS SHOWN BELOW.WHICH OF THEM WILL RESENT IN THE TRANSITION OF A PHOTON OF WAVE LENGTH 275mm?</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBan-OOivPwwQVBoE2nH5qQ6wZa7UeeAK1bT0-EFWzFwPzYAufgPjtdCZLKp91Qg-jeOdMOT0H476GTLjdWsG95Pw5vvjeDyaj26KI5-f-EeUWDnDXFY8-epc5wimSBHrik_OrP4b1Gw3w/s1600/New+Picture+%283%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBan-OOivPwwQVBoE2nH5qQ6wZa7UeeAK1bT0-EFWzFwPzYAufgPjtdCZLKp91Qg-jeOdMOT0H476GTLjdWsG95Pw5vvjeDyaj26KI5-f-EeUWDnDXFY8-epc5wimSBHrik_OrP4b1Gw3w/s1600/New+Picture+%283%29.png" /></a></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: justify; text-indent: -0.5in;"><br />
</div><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-align: center; text-indent: -0.5in;"></div><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Q10 WHATE IS MEANT BY BINDING ENERGY OF DEUTRON(<sub>1</sub>H<sup>2</sup>)AND α-PARTICLE (<sub>2</sub>He<sup>4</sup>) are 1.25 and 7.2 Mev/ NUCLEON RESPECTIVELY.WHICH</span></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0tag:blogger.com,1999:blog-4369263199692872808.post-2598195415672211522012-03-10T16:46:00.000-08:002012-03-10T16:46:16.200-08:00IMPORTANT QUESTIONS OF ELECTROSTATICS<div dir="ltr" style="text-align: left;" trbidi="on"><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves/> <w:TrackFormatting/> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:DoNotPromoteQF/> <w:LidThemeOther>EN-US</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> <w:SplitPgBreakAndParaMark/> <w:DontVertAlignCellWithSp/> <w:DontBreakConstrainedForcedTables/> <w:DontVertAlignInTxbx/> <w:Word11KerningPairs/> <w:CachedColBalance/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> <m:mathPr> <m:mathFont m:val="Cambria Math"/> <m:brkBin m:val="before"/> <m:brkBinSub m:val="--> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><!--[endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
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</style> <![endif]--> <div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="color: red; font-size: 14pt; line-height: 150%;"><span> </span><b><u>IMPORTANT QUESTIONS</u></b></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">Q.1-</span></u></b><u><span style="font-size: 14pt; line-height: 150%;"><span> </span></span></u><span style="color: blue; font-size: 14pt; line-height: 150%;">Give two properties of electric lines of force sketch them for an isolated positive charge ?</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">Q.2- </span></u></b><span style="color: blue; font-size: 14pt; line-height: 150%;">Derive an expression for dipole field intensity at any point on – (a)- axial line of dipole </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="color: blue; font-size: 14pt; line-height: 150%;"><span> </span>(b)- equatorial line of dipole.</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">Q.3-</span></u></b><span style="color: blue; font-size: 14pt; line-height: 150%;">Derive an expression for torque acting<span> </span>on<span> </span>an electric dipole in a uniform electric field.</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">Q.4-</span></u></b><span style="color: blue; font-size: 14pt; line-height: 150%;">Define capacitance and write its S.I. unit .</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">Q.5-</span></u></b><span style="color: blue; font-size: 14pt; line-height: 150%;"> Define an expression for the capacitance<span> </span>of a parallel plate capacitor.</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">Q.6- </span></u></b><span style="color: blue; font-size: 14pt; line-height: 150%;">Prove that energy density stored in parallel plate capacitor is1/2</span><span style="font-size: 14pt; line-height: 150%;"> <span style="color: blue;">є<sub>0</sub>E<sup>2<span> </span></sup>where symbols have their usual meaning.</span></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">Q.7-<span> </span></span></u></b><span style="color: blue; font-size: 14pt; line-height: 150%;">Derive an expression for energy stored in parallel plate capacitor . What is the form of this energy & where from it comes .</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">Q.8-<span> </span></span></u></b><span style="color: blue; font-size: 14pt; line-height: 150%;">Find an expression for capacitance of parallel plate capacitor when dielectric slab is introduced between the plates of the capacitor .</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">Q.9-<span> </span></span></u></b><span style="color: blue; font-size: 14pt; line-height: 150%;">It states gauss’s law in electrostatics. Using this law derive an expression for electric field due to charged spherical shell.</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">Q.10- </span></u></b><span style="color: blue; font-size: 14pt; line-height: 150%;">Draw the level diagram of Van de graff generator . Explain the principle, working of<span> </span>Van de graff generator.</span></div></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0tag:blogger.com,1999:blog-4369263199692872808.post-3419263897607803572012-03-10T16:44:00.000-08:002012-03-10T16:44:47.823-08:00VAN DE GRAFF GENERATOR<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGOF2tTEinOnHrSaFSrJlSquj-g4V7eBwkVmk9YJQXMnEp8wE4l9ez8Wn5W2ex1qPbYPODpaMkuevi0j_ViVw3OCi_cLSF90XfZaIj9MjfQnEir2gOfEgmtPercu36J47E_7fqZ4jycYUC/s1600/New+Picture+%25286%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="271" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGOF2tTEinOnHrSaFSrJlSquj-g4V7eBwkVmk9YJQXMnEp8wE4l9ez8Wn5W2ex1qPbYPODpaMkuevi0j_ViVw3OCi_cLSF90XfZaIj9MjfQnEir2gOfEgmtPercu36J47E_7fqZ4jycYUC/s320/New+Picture+%25286%2529.png" width="320" /></a></div><!--[if !mso]> <style>
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</div><div align="center" class="MsoNormal" style="line-height: 150%; margin-top: 12pt; text-align: center;"><span style="font-size: 14pt; line-height: 150%;"></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">It was designed by Vande graff in the year 1931</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">PRINCIPLE-</span></u></b><span style="font-size: 14pt; line-height: 150%;"><span> </span>The generator is based on –</span></div><div class="MsoNormal" style="line-height: 150%; margin: 12pt 0in 0.0001pt 21.75pt; text-indent: -21.75pt;"><span style="font-size: 14pt; line-height: 150%;"><span>1-<span style="font: 7pt "Times New Roman";"> </span></span></span><span style="font-size: 14pt; line-height: 150%;">The action of sharp points<span> </span>i.e,<span> </span>phenomenon of <u>CORONA DISCHARGE</u></span></div><div class="MsoNormal" style="line-height: 150%; margin: 12pt 0in 0.0001pt 21.75pt; text-indent: -21.75pt;"><span style="font-size: 14pt; line-height: 150%;"><span>2-<span style="font: 7pt "Times New Roman";"> </span></span></span><span style="font-size: 14pt; line-height: 150%;">The property that charge is given to a hollow conductor is transferred to outer surface and distributed informally over it.</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">It is machine capable of building up a potential difference of few million volts & field close to the break down field of air which is about 3×10<sup>8</sup> V/m</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>A large spherical conducting shell (few meters radius ) is supported at height several meters above the ground on the insulating column.</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">A long narrow endless belt insulating material like rubber or silk is wound around two pulleys . One at ground level , one at the centre of the shell. This belt is kept continuously<span> </span>moving by motor driving the lower pulley . It continuously carries positive sprayed on to it by a brush at ground level to the top up. There it transfers its positive charge to another conducting brush connected to the large shell. Thus the positive charge is transferred to the shell where it spread out on the outer surface.</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">Application-</span></u></b><span style="font-size: 14pt; line-height: 150%;"> Accelerated positive charge are used to carried out nuclear reactions. </span></div></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0tag:blogger.com,1999:blog-4369263199692872808.post-51567088715478894722012-03-10T16:33:00.000-08:002012-03-10T16:33:33.752-08:00APPLICATION OF GAUSS LAW<div dir="ltr" style="text-align: left;" trbidi="on"><!--[if !mso]> <style>
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<div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: red; font-size: 14pt; line-height: 150%;">CAPACITANCE OF A PARALLEL PLATE CAPACITOR WHEN DIELECTRIC SLAB IS INTRODUCED BETWEEN THE SLAB </span></u></b></div><div align="center" class="MsoNormal" style="line-height: 150%; margin-top: 12pt; text-align: center;"><b><span style="color: red; font-size: 14pt; line-height: 150%;"></span></b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9pP7zmmhcrpEaXK6GPM3SjikGw08z23xB0M0Kra2ZFKvq28ZRMGtXUqOQprMC0LCz-AEpwr8jHyVxYUnbXC7DCIMoyUv2jHTSqScFT3809ED3sBtTmbuai34siYuIhWs9C663O679Gup9/s1600/New+Picture+%284%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9pP7zmmhcrpEaXK6GPM3SjikGw08z23xB0M0Kra2ZFKvq28ZRMGtXUqOQprMC0LCz-AEpwr8jHyVxYUnbXC7DCIMoyUv2jHTSqScFT3809ED3sBtTmbuai34siYuIhWs9C663O679Gup9/s320/New+Picture+%284%29.png" width="320" /></a></div><div align="center" class="MsoNormal" style="line-height: 150%; margin-top: 12pt; text-align: center;"><span style="font-size: 14pt; line-height: 150%;">LET ,E<sub>0</sub> is applied electric field</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>E<sub>0 </sub><span> </span>=<span> </span>q/ є<sub>0</sub>A<span> </span>-----------------------(1)</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>E = Induced electric field</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>Potential difference across the capacitor </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>V = E<span> </span>×t + E<sub>0</sub> (d-t)</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>From definition of dielectric constant </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>K = E<sub>0</sub> / E</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>Or<span> </span>E = E<sub>0</sub>/K</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>On substituting the value of E</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>V =<span> </span>E<sub>0</sub>t/K + <sub><span> </span></sub>E<sub>0</sub> (d-t)</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>V<span> </span>= E<sub>0</sub> [t/k + (d-t)]<span> </span><span> </span>-------------------(2)</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>As<span> </span>c= q/V<span> </span>----------------------(3)</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>Now from equation (1)<span> </span>in (2)</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>V = q/ є<sub>0</sub>A<span> </span>[t/k + (d-t)]<span> </span>----------------(4)<span> </span></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">Now, Equation (4) in (3)</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span><span> </span>c = q/ (q/ є<sub>0</sub>A<span> </span>[t/k + (d-t)])<span> </span></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>c = є<sub>0</sub>A/[t/k + (d-t)]<span> </span></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>If<span> </span>t = d</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>So<span> </span>c = k є<sub>0</sub>A/d</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">When battery is removed & dielectric slab is introduced the charge will be same.</span></div></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0tag:blogger.com,1999:blog-4369263199692872808.post-75462329133244835792012-03-10T16:29:00.000-08:002012-03-10T16:29:17.680-08:00APPLICATION OF GAUSS LAW<div dir="ltr" style="text-align: left;" trbidi="on"><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves/> <w:TrackFormatting/> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:DoNotPromoteQF/> <w:LidThemeOther>EN-US</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> <w:SplitPgBreakAndParaMark/> <w:DontVertAlignCellWithSp/> <w:DontBreakConstrainedForcedTables/> <w:DontVertAlignInTxbx/> <w:Word11KerningPairs/> <w:CachedColBalance/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> <m:mathPr> <m:mathFont m:val="Cambria Math"/> <m:brkBin m:val="before"/> <m:brkBinSub m:val="--> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><!--[endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
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<br />
<div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><span style="color: blue; font-size: 14pt; line-height: 150%;">ENERGY DENSITY STORED BETWEEN THE PLATE OF THE CAPACITOR</span></b></div><br />
<br />
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<div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">Suppose the conductor is charged gradually at any stage , the charge on the conductor is q </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">Potential difference (v) = q/c </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">Small amount of work done in given an additional charge dq to the conductor </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>dw = q/c × dq</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">Total work done in giving a charge Q to the conductor<span> </span>is under limit q=Q,q=0</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>W =<span> </span></span><span style="font-size: 20pt; line-height: 150%;">∫</span><span style="font-size: 14pt; line-height: 150%;"> q/c dq<span> </span>= 1/c [q<sup>2</sup>/2]<sup>q=Q</sup><sub>q=0</sub></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>W = 1/c × Q<sup>2</sup>/2</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>Energy stored in the conductor </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>U = W = 1/c × Q<sup>2</sup>/2</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>As<span> </span>Q = cV</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>So<span> </span>U = 1/2 × (cV)<sup> 2</sup>/c = 1/2 cV<sup>2</sup></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><sup><span style="font-size: 14pt; line-height: 150%;"><span> </span></span></sup><span style="font-size: 14pt; line-height: 150%;">cV = Q ,<span> </span>W = ½ QV</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">Energy density is defined as total energy stored per unit volume of the conductor</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span><span> </span>u = total energy / volume</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>= 1/2 cV<sup>2</sup>/Ad</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>c = є<sub>0</sub>A/d<span> </span>and<span> </span>V = E . d</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>=<span> </span>½<span> </span>(є<sub>0</sub>A/d<span> </span>) (E<sup>2</sup> d<sup>2</sup>/Ad)</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>Energy density = 1/2 є<sub>0</sub> E<sup>2</sup></span></div><br />
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</div></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0tag:blogger.com,1999:blog-4369263199692872808.post-70967054266260991562012-03-10T16:22:00.000-08:002012-03-10T16:22:22.781-08:00<div dir="ltr" style="text-align: left;" trbidi="on"><!--[if !mso]> <style>
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<div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span><b><u><span style="color: blue;">CAPACITOR -<span> </span></span></u></b>Capacitor is a system of two conductors separated by an insulator. The conductors have charges +Q and –Q and potential V<sub>1<span> </span></sub>and V<sub>2</sub></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>Q <img height="17" src="file:///C:/DOCUME%7E1/AMITGA%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.jpg" width="16" /><span> </span>V </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>c = Q / V<span> </span>, the constant c is called capacitance of the capacitor. Capacitance c depends only on the geometrical configuration (shape , size , separation of the two conductors .)</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>S.I. unit of capacitance is ‘FARAD’ (F)</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><i><u><span style="font-size: 14pt; line-height: 150%;">DEFINATION<span> </span>OF 1 FARAD –</span></u></i></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>1F = 1 C/V</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>1µF = 10<sup>-6 </sup>F<span> </span>&<span> </span>1pF = 10<sup>-12</sup>F</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">PARALLEL PLATE CAPACITOR - </span></u></b><span style="font-size: 14pt; line-height: 150%;"></span></div><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0.25in; text-align: center;"><span style="font-size: 14pt; line-height: 150%;"></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">The electric field in<span> </span>outer region 1</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIppKCcbTxhdjEH4gn8KaLROdOSqSiPtbw7ZNyYrcILd_WRWEHFYO6BlDsNryFW7oMNvrnPIe60ecSpZpGIBgBcXeceQBVIH9O_Tkp4uCq4Mi2WKzIiV3_Ud3SWfMZ6pbZT9vco1qgjzVq/s1600/New+Picture+%282%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="195" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIppKCcbTxhdjEH4gn8KaLROdOSqSiPtbw7ZNyYrcILd_WRWEHFYO6BlDsNryFW7oMNvrnPIe60ecSpZpGIBgBcXeceQBVIH9O_Tkp4uCq4Mi2WKzIiV3_Ud3SWfMZ6pbZT9vco1qgjzVq/s320/New+Picture+%282%29.png" width="320" /></a></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><sup><span style="font-size: 14pt; line-height: 150%;"><span> </span></span></sup><span style="font-size: 14pt; line-height: 150%;">E<sup> </sup>= σ</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> /2</span><span style="font-size: 14pt; line-height: 150%;">є<sub>0</sub> -</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> </span><span style="font-size: 14pt; line-height: 150%;">σ</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> /2</span><span style="font-size: 14pt; line-height: 150%;">є<sub>0<span> </span></sub>= 0 </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">The electric field outer region 2</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span><sup><span> </span></sup>E<sup> </sup>= σ</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> /2</span><span style="font-size: 14pt; line-height: 150%;">є<sub>0</sub> -</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> </span><span style="font-size: 14pt; line-height: 150%;">σ</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;">/2</span><span style="font-size: 14pt; line-height: 150%;">є<sub>0<span> </span></sub>= 0 </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>Electric field in the inner region between the plates 1 and 2 </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>E<sup> </sup>= σ</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> /2</span><span style="font-size: 14pt; line-height: 150%;">є<sub>0</sub> +</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> </span><span style="font-size: 14pt; line-height: 150%;">σ</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> /2</span><span style="font-size: 14pt; line-height: 150%;">є<sub>0<span> </span></sub>= Q/ є<sub>0</sub>A</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>V = E . d = 1/ є<sub>0 </sub>× Qd/ A</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>The capacitance C on the parallel plate capacitor is</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>c = Q/V = є<sub>0</sub>A/d</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>c = є<sub>0</sub>A/d</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>c depends on the factors </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>1-<span> </span>c<span> </span><img height="17" src="file:///C:/DOCUME%7E1/AMITGA%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.jpg" width="16" /><span> </span>A</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>2-<span> </span>c <img height="17" src="file:///C:/DOCUME%7E1/AMITGA%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.jpg" width="16" /><span> </span>1/d</span></div></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0tag:blogger.com,1999:blog-4369263199692872808.post-6292895869962999812012-03-10T16:19:00.000-08:002012-03-10T16:19:12.607-08:00APPLICATION OF GAUSS LAW<div dir="ltr" style="text-align: left;" trbidi="on"> <!--[if !mso]> <style>
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<div class="MsoNormal" style="line-height: 150%;"><b><u><span style="color: blue; font-size: 14pt; line-height: 150%;">FIELD DUE TO UNIFORMLY CHARGED THIN SPHERICAL SHELL </span></u></b><b><span style="color: blue; font-size: 14pt; line-height: 150%;">:</span></b><span style="color: blue; font-size: 14pt; line-height: 150%;"></span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 391.7pt; text-indent: -391.7pt;"><u><span style="font-size: 14pt; line-height: 150%;">(1)Field out side the shell</span></u><span style="font-size: 14pt; line-height: 150%;"></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDzKQthX6zxActxtWSaKqun5Ek3dbOdXJLr0FeIxO1lsOIXaBfHLCp50Ta4OVXokupeaXPcVtaC5Rsd9_0xalKDgI97hLwvzoaN_g3cAFxSxX58I4GSLDDK2xdzHzOLKGtrccqG-n4MAIm/s1600/New+Picture.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="231" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDzKQthX6zxActxtWSaKqun5Ek3dbOdXJLr0FeIxO1lsOIXaBfHLCp50Ta4OVXokupeaXPcVtaC5Rsd9_0xalKDgI97hLwvzoaN_g3cAFxSxX58I4GSLDDK2xdzHzOLKGtrccqG-n4MAIm/s320/New+Picture.png" width="320" /></a></div><div align="center" class="MsoNormal" style="line-height: 150%; margin-top: 12pt; text-align: center;"><span style="font-size: 14pt; line-height: 150%;">Flux through Gaussian surface = E×4</span>π<span style="font-size: 14pt; line-height: 150%;">r<sup>2</sup> </span></div><div align="center" class="MsoNormal" style="line-height: 150%; margin-top: 12pt; text-align: center;"><span style="font-size: 14pt; line-height: 150%;">Charge enclosed =σ×4</span>π<span style="font-size: 14pt; line-height: 150%;">R<sup>2<span> </span></sup><span></span> </span></div><div align="center" class="MsoNormal" style="line-height: 150%; margin-top: 12pt; text-align: center;"><span style="font-size: 14pt; line-height: 150%;">By Gaussian’slaw<span> </span></span></div><div align="center" class="MsoNormal" style="line-height: 150%; margin-top: 12pt; text-align: center;"><span style="font-size: 14pt; line-height: 150%;"><span></span>E×4</span>π<span style="font-size: 14pt; line-height: 150%;">r<sup>2</sup> = σ</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> /</span><span style="font-size: 14pt; line-height: 150%;">є<sub>0 </sub>×4R</span>π<sup><span style="font-size: 14pt; line-height: 150%;">2<span> </span></span></sup><span style="font-size: 14pt; line-height: 150%;"></span></div><div align="center" class="MsoNormal" style="line-height: 150%; margin-top: 12pt; text-align: center;"><span style="font-size: 14pt; line-height: 150%;">E = σ</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> R</span><sup><span style="font-size: 14pt; line-height: 150%;">2</span></sup><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;">/</span><span style="font-size: 14pt; line-height: 150%;">є<sub>0</sub> r<sup>2</sup>= q/<sup> </sup>4 є<sub>0</sub></span>π<span style="font-size: 14pt; line-height: 150%;"> r<sup>2</sup></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>Where<span> </span>q = 4</span>π<span style="font-size: 14pt; line-height: 150%;">R<sup>2</sup> σ</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"><span> </span></span><span style="font-size: 14pt; line-height: 150%;">is the total charge on the spherical<span> </span>Vectorially<span> </span></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>E = q/<sup> </sup>4є<sub>0</sub> </span>π<span style="font-size: 14pt; line-height: 150%;">r<sup>2 </sup>r^</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">(2) <b><u>Field inside the shell</u></b></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;">However in this case , the Gaussian surface enclosed no charge </span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span><span> </span>Diagram</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>According to<span> </span>Gauss’s law<span> </span></span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>E×4</span><span style="font-family: "Times New Roman Special G2"; font-size: 14pt; line-height: 150%;"><span>_</span></span><span style="font-size: 14pt; line-height: 150%;">r<sup>2</sup> = 0</span></div><div class="MsoNormal" style="line-height: 150%; margin-top: 12pt;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>E = 0<span> </span>(r<R)</span></div></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0tag:blogger.com,1999:blog-4369263199692872808.post-85720155987260185672012-03-09T03:35:00.000-08:002012-03-09T03:35:28.961-08:00APPLICATION OF GAUSS LAW<div dir="ltr" style="text-align: left;" trbidi="on"><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves/> <w:TrackFormatting/> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:DoNotPromoteQF/> <w:LidThemeOther>EN-US</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> <w:SplitPgBreakAndParaMark/> <w:DontVertAlignCellWithSp/> <w:DontBreakConstrainedForcedTables/> <w:DontVertAlignInTxbx/> <w:Word11KerningPairs/> <w:CachedColBalance/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> <m:mathPr> <m:mathFont m:val="Cambria Math"/> <m:brkBin m:val="before"/> <m:brkBinSub m:val="--> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><!--[endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
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</style> <![endif]--> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-size: 14pt; line-height: 150%;">Electric flux through Gaussian surface = flux through the curved cylindrical part of the surface</span></div><div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-size: 14pt; line-height: 150%;">=E</span><span style="font-family: "Arial Black","sans-serif"; font-size: 14pt; line-height: 150%; text-transform: uppercase;">×2</span>π<span style="font-family: "Arial Black","sans-serif"; font-size: 14pt; line-height: 150%;">rl</span></div><div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><br />
</div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;">Surface includes charge<span> </span>λl</span></div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>Where λ is the surface charge density </span></div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>E</span><span style="font-family: "Arial Black","sans-serif"; font-size: 14pt; line-height: 150%; text-transform: uppercase;">×2</span>π<span style="font-family: "Arial Black","sans-serif"; font-size: 14pt; line-height: 150%;">rl </span><span style="font-size: 14pt; line-height: 150%;">= λl / є<sub>0</sub></span></div><div class="MsoNormal" style="line-height: 150%;"><sub><span style="font-size: 14pt; line-height: 150%;"><span> </span></span></sub><span style="font-size: 14pt; line-height: 150%;"><span> </span>E =λ/2 πє<sub>0</sub> r</span></div><div class="MsoNormal" style="line-height: 150%;"><br />
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<div class="MsoNormal" style="line-height: 150%;"><b><u><span style="font-size: 14pt; line-height: 150%;">GAUSS LAW IN ELECTROSTATICS –</span></u></b></div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;">Electric flux through a closed surface ‘S’ is 1/ є<sub>0 </sub><span> </span>times the total charge enclosed by ‘S’</span></div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>Electric flux (φ) =q/є<sub>0</sub></span></div><div class="MsoNormal" style="color: black; line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;"> ⌠E.ds = </span><span style="font-size: 14pt; line-height: 150%;">q/є<sub>0</sub></span></div></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0tag:blogger.com,1999:blog-4369263199692872808.post-45229851899801858412012-03-08T01:38:00.000-08:002012-03-08T01:38:18.364-08:00Electric Dipole<div dir="ltr" style="text-align: left;" trbidi="on"><!--[if !mso]> <style>
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</style> <![endif]--> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-size: 14pt; line-height: 150%; text-transform: uppercase;">magnitude of torque = force</span><span style="font-family: "Arial Black","sans-serif"; font-size: 14pt; line-height: 150%; text-transform: uppercase;">×┴ </span><span style="font-size: 14pt; line-height: 150%;">distance</span><span style="font-family: "Arial Black","sans-serif"; font-size: 14pt; line-height: 150%; text-transform: uppercase;"><span> </span></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzGr9WEQ3_f-yUGktQfFMmuNhfrgwsBVgF-h0mVFn9ePzYCIkk96TLcSCoZV95OnfFN32188NqrPrEuIokqhcyVB99Eyzx1hi5K2Jf7GpRHnOGwpAxHP0bmeUPsEVMpe2sRfZwAo2rBtW1/s1600/New+Picture+%283%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="209" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzGr9WEQ3_f-yUGktQfFMmuNhfrgwsBVgF-h0mVFn9ePzYCIkk96TLcSCoZV95OnfFN32188NqrPrEuIokqhcyVB99Eyzx1hi5K2Jf7GpRHnOGwpAxHP0bmeUPsEVMpe2sRfZwAo2rBtW1/s320/New+Picture+%283%29.png" width="320" /></a></div><div class="MsoNormal" style="line-height: 150%;"><br />
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</style> <![endif]--> <div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;">The net flux through the Gaussian surface is 2EA </span></div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;">The charge enclosed by the closed surface is σ A </span></div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>By applying Gauss’s law </span></div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>2EA =<span> </span>σA/ є<sub>0</sub></span></div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>Or<span> </span>E =<span> </span>σ</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> /</span><span style="font-size: 14pt; line-height: 150%;">2 є<sub>0</sub></span></div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>In vector form </span></div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;"><span> </span>E = σ</span><span style="font-family: "Elephant","serif"; font-size: 14pt; line-height: 150%;"> /</span><span style="font-size: 14pt; line-height: 150%;">2 є<sub>0</sub><span> </span>n^</span></div><div class="MsoNormal" style="line-height: 150%;"><span style="font-size: 14pt; line-height: 150%;"><span> </span><span> </span>E = σ R<sup>2</sup>/ є<sub>0</sub> r<sup>2 </sup>= q/4Пє<sub>0</sub> r<sup>2 </sup></span></div><div class="MsoNormal" style="line-height: 150%;"><br />
</div><div class="MsoNormal" style="line-height: 150%;"><br />
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</div></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com2tag:blogger.com,1999:blog-4369263199692872808.post-29269165515851919212012-03-01T02:03:00.000-08:002012-03-01T02:03:43.957-08:00PROPERTIES OF ELECTRIC FIELD LINES :<div dir="ltr" style="text-align: left;" trbidi="on"><br />
<div class="MsoNormal" style="margin-left: 25.5pt; text-indent: -0.25in;"><span style="font-size: 14pt;">1-<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 14pt;">Field lines start from positive charges and end at negative charges . </span></div><div class="MsoNormal" style="margin-left: 25.5pt; text-indent: -0.25in;"><span style="font-size: 14pt;">2-<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 14pt;">Two field lines can never cross each other ( If they did, the field at the point of intersection will not have unique direction which is absurd)</span></div><div class="MsoNormal" style="margin-left: 7.5pt;"><span style="font-size: 14pt;">3-<span style="font: 7pt "Times New Roman";"> </span></span><span style="font-size: 14pt;">Electrostatics field lines do not form any closed loop.<br />
<a name='more'></a></span></div><div class="MsoNormal" style="margin-left: 7.5pt;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5tU0dKxCsPmkUg8GGhGShcK3kNHPuO9_YVApDgA7_WoEdapEMI5TifO-pLopVDJCrJJJvi91fmahHCGLEgWgUfGFlhXRjB9CZhRl9OrVatc1caQ0MtG-mTWVfr3IEDD1SE7yj0CMqG4Fe/s1600/untitled.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="312" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5tU0dKxCsPmkUg8GGhGShcK3kNHPuO9_YVApDgA7_WoEdapEMI5TifO-pLopVDJCrJJJvi91fmahHCGLEgWgUfGFlhXRjB9CZhRl9OrVatc1caQ0MtG-mTWVfr3IEDD1SE7yj0CMqG4Fe/s320/untitled.bmp" width="320" /></a></div><br />
</div><span style="font-family: "Times New Roman"; font-size: 14pt;"> </span></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0tag:blogger.com,1999:blog-4369263199692872808.post-52816840790342644832012-02-29T19:24:00.000-08:002012-02-29T19:24:05.002-08:00Coulomb’s Law<div dir="ltr" style="text-align: left;" trbidi="on"><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><!--[if gte mso 10]> <style>
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<div class="MsoNormal"><b><u><span style="font-size: 14pt;">Coulomb’s Law- <span style="color: black;"><span> </span></span></span></u></b><span style="color: black; font-size: 14pt;">It states that force between two point charges is directly proportional to the product of<span> </span>the magnitude of two charges & inversely proportional to the square of distance between them . The direction of<span> </span>force is along<span> </span>the line joining two point charges.</span></div><div class="MsoNormal"><span style="color: black; font-size: 14pt;"><span> </span><i>Mathematically,</i></span></div><div class="MsoNormal"><i><span style="color: black; font-size: 14pt;"><span> </span></span></i><span style="color: black; font-size: 14pt;">F </span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>µ</span></span><span style="color: black; font-size: 14pt;"> q<sub>1</sub> q<sub>2</sub>/r<sup>2</sup><span> </span>q<sub>1</sub></span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>·</span></span><span style="color: black; font-size: 14pt;">----------------------------------</span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>·</span></span><span style="color: black; font-size: 14pt;">q<sub>2</sub></span></div><div class="MsoNormal"><span style="color: black; font-size: 14pt;"><span> </span>F = k q<sub>1</sub> q<sub>2</sub>/r<sup>2 </sup><span> </span><sup><span> </span></sup><span> </span><sup><span> </span>______________<span> </span>r<span> </span>_________________<span> </span></sup></span></div><div class="MsoNormal"><b><u><span style="color: black; font-size: 14pt;">Case 1-</span></u></b><span style="color: black; font-size: 14pt;"><span> </span>When medium between two charges is air/vacuum/free space </span></div><div class="MsoNormal"><span style="color: black; font-size: 14pt;"><span> </span>k = 1/4</span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>Õ</span></span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>e</span></span><sub><span style="color: black; font-size: 14pt;">o</span></sub><span style="color: black; font-size: 14pt;"><span> </span></span></div><div class="MsoNormal"><span style="color: black; font-size: 14pt;"><span> </span>then<span> </span>F =<span> </span>1/4</span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>Õ</span></span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>e</span></span><sub><span style="color: black; font-size: 14pt;">o</span></sub><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>´</span></span><span style="color: black; font-size: 14pt;"> q<sub>1</sub> q<sub>2</sub>/r<sup>2</sup><span> </span>(</span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>e</span></span><sub><span style="color: black; font-size: 14pt;">o = 8</span></sub><b><sub><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>×</span></span></sub></b><sub><span style="color: black; font-size: 14pt;">854 </span></sub><sub><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>´</span></span></sub><sub><span style="color: black; font-size: 14pt;">10</span></sub><sup><span style="color: black; font-size: 14pt;">-12</span></sup><span style="color: black; font-size: 14pt;"> C<sup>2</sup>N<sup>-1</sup>m<sup>-2</sup> )<sup> </sup></span></div><div class="MsoNormal"><b><u><span style="color: black; font-size: 14pt;">Case 2-<span> </span></span></u></b><span style="color: black; font-size: 14pt;">When medium between two charges is other than air </span></div><div class="MsoNormal"><span style="color: black; font-size: 14pt;"><span> </span>k = 1/4</span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>Õ</span></span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>e</span></span><span style="font-size: 14pt;"></span></div><div class="MsoNormal"><span style="color: black; font-size: 14pt;"><span> </span>Then<span> </span>F = 1/4</span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>Õ</span></span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>e</span></span><span style="color: black; font-size: 14pt;"> </span><span style="color: black; font-family: Symbol; font-size: 14pt;"><span>´</span></span><span style="color: black; font-size: 14pt;"> q<sub>1</sub> q<sub>2</sub>/r<sup>2</sup><span> </span></span></div><div class="MsoNormal"><u><span style="color: black; font-size: 14pt;">__________________________________________________________________________</span></u></div><div class="MsoNormal"><span style="color: black; font-size: 14pt;"><span> </span></span><b><u><span style="color: magenta; font-size: 14pt;">QUESTION</span></u></b><i><u><span style="color: magenta; font-size: 14pt;">-</span></u></i><i><span style="font-size: 14pt;"><span> </span><b><span style="color: blue;">A</span></b> <b><span style="color: blue;">charge q is placed at the centre of line joining two equal charges Q. Show that the system of three charges will be in equilibrium if q = -Q/4 ?</span></b></span></i></div><div class="MsoNormal"><b><i><u><span style="color: magenta; font-size: 14pt;">SOLUTION-</span></u></i></b><span style="font-size: 14pt;"> <b><i><span style="color: blue;">Let two equal charges<span> </span>Q each be held A and B , where AB = 2x & C is the centre of AB , where q is held<span> </span></span><span> </span><sup>______________<span> </span>2x<span> </span>_________________<span> </span></sup></i></b></span></div><div class="MsoNormal"><b><i><span style="font-size: 14pt;"><span> </span></span></i></b><b><i><span style="font-family: Symbol; font-size: 14pt;"><span>·</span></span></i></b><b><i><span style="font-size: 14pt;">-----------------</span></i></b><b><i><span style="font-family: Symbol; font-size: 14pt;"><span>·</span></span></i></b><b><i><span style="font-size: 14pt;">-----------------</span></i></b><b><i><span style="font-family: Symbol; font-size: 14pt;"><span>·</span></span></i></b><b><i><span style="font-size: 14pt;"> </span></i></b></div><div class="MsoNormal"><b><i><span style="color: blue; font-size: 14pt;"><span> </span><span> </span>A<span> </span>C<span> </span>B</span></i></b></div><div class="MsoNormal"><b><i><span style="color: blue; font-size: 14pt;"><span> </span></span></i></b></div><div class="MsoNormal"><b><i><span style="color: blue; font-size: 14pt;"><span> </span>Net force on q is zero, so q is already is in equilibrium</span></i></b></div><div class="MsoNormal"><b><i><span style="color: blue; font-size: 14pt;"><span> </span>Now total charge on Q at B</span></i></b></div><div class="MsoNormal"><b><i><span style="color: blue; font-size: 14pt;"><span> </span>1/4</span></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>Õ</span></span></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>e</span></span></i></b><b><i><sub><span style="color: blue; font-size: 14pt;"> o</span></sub></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>´</span></span></i></b><b><i><span style="color: blue; font-size: 14pt;">Qq/x<sup>2</sup> +<span> </span>1/4</span></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>Õ</span></span></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>e</span></span></i></b><b><i><sub><span style="color: blue; font-size: 14pt;"> o</span></sub></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>´</span></span></i></b><b><i><span style="color: blue; font-size: 14pt;">QQ/(2x)<sup>2</sup> = 0</span></i></b></div><div class="MsoNormal"><b><i><span style="color: blue; font-size: 14pt;"><span> </span>1/4</span></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>Õ</span></span></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>e</span></span></i></b><b><i><sub><span style="color: blue; font-size: 14pt;"> o</span></sub></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>´</span></span></i></b><b><i><span style="color: blue; font-size: 14pt;">Qq/x<sup>2</sup> =-1/4</span></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>Õ</span></span></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>e</span></span></i></b><b><i><sub><span style="color: blue; font-size: 14pt;"> o</span></sub></i></b><b><i><span style="color: blue; font-family: Symbol; font-size: 14pt;"><span>´</span></span></i></b><b><i><span style="color: blue; font-size: 14pt;">QQ/(2x)<sup>2</sup> </span></i></b></div><div class="MsoNormal"><b><i><span style="color: blue; font-size: 14pt;"><span> </span><u>So<span> </span>q =<span> </span>-Q/4<span> </span>(HENCE PROVED)</u></span></i></b></div></div>आप और हमhttp://www.blogger.com/profile/00422902025702838157noreply@blogger.com0