A capacitor consists of a flat plate of area A and another plate with a stair-like geometry, as depicted in the figure. Each stair has a width a and a height b . Determine the capacitance of this assembly.

Step-by-step solution

The given capacitor can be considered as a parallel combination of three smaller capacitors. The total area of the flat plate is A and its total length is 3a . Therefore, the area of each stair section of width a is A 3 . The distances between the plates for the three sections are d , d+b , and d+2b . The capacitances of the three sections are: C₁ = ₀ (A/3) d C₂ = ₀ (A/3) d+b C₃ = ₀ (A/3) d+2b Since the three capacitors are connected in parallel, the equivalent capacitance is: C_ eq = C₁ + C₂ + C₃ C_ eq = ₀ A 3 ( 1