A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect ?

A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect ?

(a) The energy stored in the capacitor decreases \( K \) times.

(b) The change in energy stored is \( \frac{1}{2} C V^2 \left( \frac{1}{K} - 1 \right) \)

(c) The charge on the capacitor is not conserved.

(d) The potential difference between the plates decreases \( K \) times.

Answer :  (c) The charge on the capacitor is not conserved.

\( U = \frac{U_0}{K} \Rightarrow \) The energy stored in the capacitor decreases \( K \) times.

\( \frac{U_0}{K} - U_0 \Rightarrow \) The change in energy stored is \( \frac{1}{2} C V^2 \left( \frac{1}{K} - 1 \right) \)

\( V = \frac{V_0}{K} \Rightarrow \) The potential difference between the plates decreases \( K \) times.