A capacitor C is fully charged with voltage V0.

A capacitor C is fully charged with voltage V0. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance C/2. The energy loss in the process after the charge is distributed between the two capacitors is:

1) \(\frac{1}{2}CV_{0}^{2}\)

2) \(\frac{1}{4}CV_{0}^{2}\)

3) \(\frac{1}{3}CV_{0}^{2}\)

4) \(\frac{1}{6}CV_{0}^{2}\)

Answer: (4)

JEE Main 2020 Physics Shift 2- 4th Sept Solved Paper

\(v_{f}=\frac{C V_{0}}{3 \frac{C}{2}}=\frac{2 V_{0}}{3}\) \(u_{i}=\frac{1}{2} C V_{0}^{2}\) \(u_{f}=\frac{1}{2}\left(\frac{3 C}{2}\right) \frac{4 V_{0}^{2}}{9}=\frac{C V_{0}^{2}}{3}\) \(u_{i}-u_{f}=\frac{1}{2} C V_{0}^{2}-\frac{C V_{0}^{2}}{3}\) \(=C V_{0}^{2}\left(\frac{1}{2}-\frac{1}{3}\right)=\frac{C V_{0}^{2}}{6}\)

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