Question

Energy E is stored in a parallel plate capacitor $C_1.$ An identical uncharged capacitor $C_3$ is connected to it, kept in contact with it for a while and then disconnected the energy stored in $C_2$ is:

• A. $\frac{E}{2}$
• B. $\frac{E}{3}$
• C. $\frac{E}{4}$
• D. zero

Answer 1

Answer: (C)

Let capacitance of a parallel plate capacitor $C_1=C$ If energy stored in capacitor $C_1$ is E. The charge on capacitor $q=\sqrt{2EC}$ $\left(\because E=\frac{1}{2}\frac{q^2}{C}\right)$ When. another uncharged capacitor $C_2$ having same capacitance C is connected to it then total charge on both capacitor = q When disconnected, the charge on each one capacitor $q=\frac{q}{2}=\frac{\sqrt{2EC}}{2}=\sqrt{\frac{EC}{2}}$ $\therefore$ Energy stored in $C_2$ $E=\frac{1}{2}\frac{q{}^2}{C}$ $=\frac{1}{2}\frac{EC}{2}\frac{1}{C}$ $E=\frac{E}{4}$