Into the gap between the plates of a parallel plate capacitor of capacitance a slab of metal is inserted halfway between the plates filling one fourth of the gap between the plates.What is the resulting new capacitance?

Question

Quizplus · Accepted Answer

When the slab of metal is inserted halfway between the plates, the distance between the plates is reduced by half. The capacitance is inversely proportional to the distance between the plates, so the capacitance is doubled. However, the slab of metal also acts as a capacitor with the remaining gap between the slab and the plate, adding a capacitance in series with the original capacitor. This effectively halves the capacitance, so the resulting capacitance is the average of the original capacitance and twice the half capacitance. Mathematically, the resulting capacitance can be expressed as:

C = (C/2 + 2C)/(1 + 2) = (5/4)C

where C is the original capacitance.

Therefore, the resulting new capacitance is 5/4 times the original capacitance, which corresponds to choice B.

Into the Gap Between the Plates of a Parallel Plate