Question

The potential difference between the plates of a condenser of capacitance $0.5\mu F$ is 100 volt. It is connected to an uncharged condenser of capacity $0.2\mu F$ by a copper wire. The loss of energy in this process will be :

• A. $0J$
• B. $0.5\times {10}^{-3}J$
• C. $0.7\times {10}^{-3}J$
• D. ${10}^{-3}J$

Answer 1

The correct option is C $0.7\times {10}^{-3}J$

Initial energy , $U_i=\frac{1}{2}{C}_1{V}_1^2=\frac{1}{2}\times 0.5\times {10}^{-6}\times (100{)}^2=2.5\times {10}^{-3}J$
After connecting another capacitor the common potential , $V_c=\frac{C_1{V}_1}{C_1+C_2}=\frac{0.5\left(100\right)}{0.5+0.2}=71.43V$
So final energy is $U_f=\frac{1}{2}(C_1+C_2)V_c^2=\frac{1}{2}\times (0.5+0.2)\times {10}^{-6}\times (71.43{)}^2=1.8\times {10}^{-3}J$.
Thus energy loss through the wire $=U_i-U_f=(2.5-1.8)\times {10}^{-3}=0.7\times {10}^{-3}J$