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QPages 165-170: Q17: HC Verma: Concepts of Physics - Volume 2 Capacitors Pages 165-170: Q17 Solution: A capacitor is made of a flat plate of area A and a second…

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. The width of each stair is a and the height is b. Find the capacitance of the assembly.

Step-by-Step Verified Solution

**Answer:** C=ϵ0A3(1d+1d+b+1d+2b)C = \frac{\epsilon_0 A}{3}\left(\frac{1}{d} + \frac{1}{d+b} + \frac{1}{d+2b}\right). **Step-by-Step Explanation:** The stair-like structure creates three capacitors in parallel, each with area A/3A/3.
C=C1+C2+C3=ϵ0A/3d+ϵ0A/3d+b+ϵ0A/3d+2bC = C_1 + C_2 + C_3 = \frac{\epsilon_0 A/3}{d} + \frac{\epsilon_0 A/3}{d+b} + \frac{\epsilon_0 A/3}{d+2b}

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