A <math> <mn>60</mn> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">F</mi> </math> capacitor is fully charged by a <math> <mn>20</mn> <mtext> </mtext> <mi mathvariant="normal">V</mi> </math> supply. It is then disconnected from the supply and is connected to another uncharged <math> <mn>60</mn> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">F</mi> </math> capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in <math> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">J</mi> </math> )

6Sol. Common potential after connection. V common = C 1 V 1 + C 2 V 2 C 1 + C 2 = 60 × 20 + 0 120 = 10 V o l t  Loss of energy = 1 2 C V 2 - 1 2 ( 2 C ) × V Common 2  = 1 2 × 60 × 10 - 12 × ( 20 ) 2 - 60 × 10 - 12 × ( 10 ) 2 = 60 × 10 - 12 ( 200 - 100 ) = 6000 × 10 - 12 = 6 n J

Ask & Answer Question

Physics NCERT Exemplar Solutions Class 11th Chapter Fifteen Electrostatics Physics Electrostatic Potential and Capacitance Physics Class 12th

A $60 p F$ capacitor is fully charged by a $20 V$ supply. It is then disconnected from the supply and is connected to another uncharged $60 p F$ capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in $n J$ )

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Sol. Common potential after connection.

$V_{common} = \frac{C_{1} V_{1} + C_{2} V_{2}}{C_{1} + C_{2}} = \frac{60 \times 20 + 0}{120} = 10 V o l t$

Loss of energy $= \frac{1}{2} {C V}^{2} - \frac{1}{2} (2 C) \times V_{Common}^{2}$

$\begin{array}{r} = \frac{1}{2} \times 60 \times 10^{- 12} \times (20)^{2} - 60 \times 10^{- 12} \times (10)^{2} \\ = 60 \times 10^{- 12} (200 - 100) \\ = 6000 \times 10^{- 12} \\ = 6 n J \end{array}$

6Sol. Common potential after connection. <math> <msub> <mrow> <mrow> <mi mathvariant="normal">V</mi> </mrow> </mrow> <mrow> <mrow> <mtext>common</mtext> <mtext> </mtext> </mrow> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">C</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <msub> <mrow> <mrow> <mtext> </mtext> <mi mathvariant="normal">V</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">C</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <msub> <mrow> <mrow> <mtext> </mtext> <mi mathvariant="normal">V</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">C</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">C</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>60</mn> <mo>×</mo> <mn>20</mn> <mo>+</mo> <mn>0</mn> </mrow> </mrow> <mrow> <mrow> <mn>120</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>10</mn> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">t</mi> </math> <div><div><picture><source srcset="" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1755768945phpM8OYqU.jpeg" alt="" width="419" height="93" loading="lazy"></picture></div></div> Loss of energy <math> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <msup> <mrow> <mrow> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">V</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>-</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mo>(</mo> <mn>2</mn> <mi mathvariant="normal">C</mi> <mo>)</mo> <mo>×</mo> <msubsup> <mrow> <mrow> <mi mathvariant="normal">V</mi> </mrow> </mrow> <mrow> <mrow> <mtext>Common</mtext> <mtext> </mtext> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> </math>  <math> <mtable columnalign="right"> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi> </mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mo>×</mo> <mn>60</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>12</mn> </mrow> </mrow> </msup> <mo>×</mo> <mo>(</mo> <mn>20</mn> <msup> <mrow> <mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>-</mo> <mn>60</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>12</mn> </mrow> </mrow> </msup> <mo>×</mo> <mo>(</mo> <mn>10</mn> <msup> <mrow> <mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi> </mi> <mo>=</mo> <mn>60</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>12</mn> </mrow> </mrow> </msup> <mo>(</mo> <mn>200</mn> <mo>-</mo> <mn>100</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi> </mi> <mo>=</mo> <mn>6000</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>12</mn> </mrow> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi> </mi> <mo>=</mo> <mn>6</mn> <mtext> </mtext> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">J</mi> </mrow> </mtd> </mtr> </mtable> </math> <div><div><picture><source srcset="" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1755768995phpx1tS3J.jpeg" alt="" width="315" height="155" loading="lazy"></picture></div></div>