A capacitor <math> <mi mathvariant="normal">C</mi> </math> is fully charged with voltage <math> <msub> <mrow> <mrow> <mi mathvariant="normal">V</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> </math> . After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance. <math> <mfrac> <mrow> <mrow> <mi>C</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> . The energy loss in the process after the charge is distributed between the two capacitor is:

<math> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> <msubsup> <mrow> <mrow> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">V</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> </math> (Electrostatics)

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Physics Class 12th physics ncert exemplar solutions class 12th chapter two Physics Electrostatic Potential and Capacitance

A capacitor $C$ is fully charged with voltage $V_{0}$ . After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance. $\frac{C}{2}$ . The energy loss in the process after the charge is distributed between the two capacitor is:

Option 1 -

$\frac{1}{6} {C V}_{0}^{2}$

Option 2 -

$\frac{1}{2} {C V}_{0}^{2}$

Option 3 -

$\frac{1}{4} {C V}_{0}^{2}$

Option 4 -

$\frac{1}{3} {C V}_{0}^{2}$ (Electrostatics)

3 Views | Posted 2 months ago

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Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 4

Detailed Solution:

Sol. $g = \frac{A x}{{(x^{2} + a^{2})}^{3 / 2}}$

$\Rightarrow \int_{v}^{0} ? d V = - \int_{x}^{\infty} ? g d x$

$\Rightarrow O - V = - [\int \frac{A x}{{(a^{2} + x^{2})}^{3 / 2}}]$

Let, $a^{2} + x^{2} = t^{2}$

$\Rightarrow 2 x d x = 2 t d t$

$\Rightarrow x d x = t d t$

$\Rightarrow V = \int \frac{A t d t}{t^{3}} \Rightarrow - \frac{A}{t} \Rightarrow - {\frac{A}{\sqrt[]{a^{2} + x^{2}}}|}_{x}^{\infty}$

$\Rightarrow V = \frac{A}{\sqrt[]{a^{2} + x^{2}}}$

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A capacitor $C$ is fully charged with voltage $V_{0}$ . After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance. $\frac{C}{2}$ . The energy loss in the process after the charge is distributed between the two capacitor is:

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A capacitor C is fully charged with voltage V 0 . After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance. C 2 . The energy loss in the process after the charge is distributed between the two capacitor is:

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A capacitor $C$ is fully charged with voltage $V_{0}$ . After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance. $\frac{C}{2}$ . The energy loss in the process after the charge is distributed between the two capacitor is: