Question

Two parallel plate capacitor of capacitances C and 2C are connected in parallel and charged to a potential difference V . If the battery
is disconnected and the space between the plate of the capacitor of capacince C is completely filled with a material of dielectric constant K, then the potential difference across the capacitor will be come

• A. $3V(K+2)$
• B. $\frac{(K+2)}{3V}$
• C. $\frac{3V}{(K+2)}$
• D. $\frac{3(K+2)}{V}$

Answer 1

The original capacitance of the parallel combination of C and 2 C is = C +2C = 3C

Total charge Q = 3CV

When the capacitor C is filled with a dielectric, its capacitance becomes KC.

Therefore, after the capacitor is filled with dielectric the capacitance of the combination, C' = KC + 2C = C (K + 2).

However, the charge remains the same, i.e. Q = 3CV

Therefore, the potential difference across the capacitors will be