A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is A/3 and the height is d, the capacitance of the arrangement is:

Question

G1 Physics · Accepted Answer

Image The three capacitors corresponding to the three stair regions are in parallel. Their areas are A/3 and separations are: d, 2d and 3d Therefore: C₁ = ε₀(A/3)/d C₂ = ε₀(A/3)/(2d) C₃ = ε₀(A/3)/(3d) Equivalent capacitance: Cₑq = C₁ + C₂ + C₃ = ε₀A/(3d)[1 + 1/2 + 1/3] = ε₀A/(3d)(11/6) = 11ε₀A/(18d)