A capacitor with capacitance \(5~\mu\text{F}\) is charged to \(5~\mu \text{C}\). If the plates are pulled apart to reduce the capacitance to \(2~\mu\text{F}\), how much work is done?
1. \( 3.75 \times 10^{-6} ~\text{J} \)
2. \( 6.25 \times 10^{-6} ~\text{J} \)
3. \( 2.55 \times 10^{-6} ~\text{J} \)
4. \( 2.16 \times 10^{-6}~\text{J} \)
 

A \(5~\mathrm{\mu F}\) capacitor is charged fully by a \(220~\text{V}\) supply. It is then disconnected from the supply and is connected in series to another uncharged \(2.5~\mathrm{\mu F}\) capacitor. If the energy change during the charge redistribution is \(\frac{X}{100}~\mathrm{J}\) then value of \(X\) to the nearest integer is:
1. \(10\)
2. \(20\)
3. \(4\)
4. \(1\)

A capacitor \(C\) is fully charged with voltage \(V_0\). After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance \(\frac{C}{2}\). The energy loss in the process after the charge is distributed between the two capacitors is: 
1. \( \frac{1}{6} C V_0^2 \)
2. \( \frac{1}{3} C V_0^2 \)
3. \( \frac{1}{4} C V_0^2 \)
4. \( \frac{1}{2} C V_0^2 \)

Two capacitors of capacitances \(C\) and \(2C\) are charged to potential differences \(V\) and \(2V\), respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:
1. \( \frac{9}{2} C V^2 \)
2. \( \frac{25}{6} C V^2\)
3. zero
4. \( \frac{3}{2} C V^2 \)

A parallel plate capacitor has plate of length ‘\(l\)’, width ‘\(w\)’ and separation of plates is ‘\(d\)’. It is connected to a battery of emf \(V\). A dielectric slab of the same thickness ‘\(d\)’ and of dielectric constant is being inserted between the plates of the capacitor. At what length of the slab inside plates, will be energy stored in the capacitor be two times the initial energy stored?
1. \(l/4\)
2. \(l/2\)
3. \(l/3\)
4. \(2l/3\)