A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25% more charge from the battery. The dielectric constant of mica is ____

Solution

Physics sir · 4 steps

The battery stays connected, so V is fixed: 25% more charge means 25% more capacitance.

1. Charge tracks capacitance. With the battery connected, V does not change, so Q = CV grows only because C grows. Drawing 25% more charge means C' = 1.25 C.
2. Slab capacitance. A slab of thickness t and dielectric constant K acts like a smaller air gap. The gap d is replaced by d - t + t/K.

   C'/C = d/(d - t + t/K) = 1.25

3. Put in numbers. The effective gap must be 5/1.25 = 4 mm. So 5 - 2 + 2/K = 4, which gives 2/K = 1.
4. So. K = 2, so the dielectric constant of mica is 2.0, option (d).

The idea to keep. Battery connected means V is constant and Q follows C. A partial slab turns the gap d into d - t + t/K. Work with that effective gap and the rest is one line.

Answer from the NTA final answer key. Solution by PrepWiser.