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In the figure, the area of each plate is A and the distance between consecutive plates is as shown in the figure. What is the effective capacitance between points A and B?

Asked in GUJCET 2019 · Capacitor networks

Figure: Capacitor networks
Answer: (3) (2ε₀A)/d

Step-by-step solution

Given: four plates 1–4 of area A, each gap d; plates 1 and 4 are joined to A, plates 2 and 3 to B.

Idea: each gap between facing plates at different potentials is a capacitor C = (ε₀A)/d.

Gap 1–2 lies between A and B: a capacitor C.

Gap 2–3 has both plates at B: no potential difference, so no capacitor.

Gap 3–4 lies between B and A: another C.

The two working gaps are in parallel: C_AB = 2C = (2ε₀A)/d.

Why the other options are wrong

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