Five conducting plates are placed face to face and equally spaced by distance d. The area of each plate is half that of the previous plate. If the area of the first plate is A, find the equivalent capacitance of the system shown.

Question

G1 Physics · Accepted Answer

The four gaps act as series capacitors. Their effective facing areas are A/2, A/4, A/8 and A/16, so 1/C = d/(ε₀A)[2+4+8+16] = 30d/(ε₀A). Hence C = ε₀A/(30d), option D.