Question

Two spherical conductors each of capacity $C$ are charged to potential $V$ and $-V$. These are then connected by means of a fine wire. The loss of energy is

• A. Zero
• B. $\frac{1}{2}C{V}^2$
• C. $C{V}^2$
• D. $2C{V}^2$

Answer 1

Answer: (C)

Using the formula.
Loss of energy,$\Delta U=\frac{C_1{C}_2{\left(V_1+V_2\right)}^2}{2(C_1+C_2})$
here, $C_1$ and $C_2$ is the capacitance of capacitors that is connected by wire and $V_1$ and $V_2$ is their respective potential.
Given, $C_1=C_2=C$ and $V_1=V_2=V$
Hence, $\Delta U=\frac{C\times C(V+V{)}^2}{2(C+C)}=C{V}^2$