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. $\frac{1}{2}CV^{2}$
• C. $CV^{2}$
• D. $2 \, CV^{2}$

Answer 1

Answer: (C)

Using the formula.
Loss of energy,$\left.\Delta U =\frac{ C _{1} C _{2}\left( V _{1}+ V _{2}\right)^{2}}{2\left( C _{1}+ C _{2}\right.}\right)$
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, $\Delta U =\frac{ C \times C ( V + V )^{2}}{2( C + C )}= CV ^{2}$