Question

A conductor of capacitance $0.5\mu F$ has been charged to 100volts. It is now connected to uncharged conductor of capacitance $0.2\mu F$. The loss in potential energy is nearly -

• A. ${7\times 10}^{-4}J$
• B. ${3.5\times 10}^{-4}J$
• C. ${14\times 10}^{-4}J$
• D. ${7\times 10}^{-3}J$

Answer 1

The correct option is A ${7\times 10}^{-4}J$

$Given:$ $C_1=0.5\mu F$

$C_1=0.5\mu F$

$v=100v$

$Solution:$ We know that,

$U=\frac{1}{2}{C}_T{V}^2$

$C_T=\frac{c_1{c}_2}{c_1+c_2}$

$=\frac{0.5\times 0.2}{0.5+0.2}\mu F$

$C_T=0.14\mu F$

$\therefore$

$U=\frac{1}{2}\times 0.14\times {100}^2$

$=0.07\times {10}^{-6}\times {10}^{4}J$

$=7\times {10}^{-2}\times {10}^{-6}\times {10}^{4}J$

$=7\times {10}^{-4}J$

$So,the$ $correct$ $option:A$