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Four metal plates are arranged as shown in the figure. Capacitance between X and Y ( A → Area of each plate, d → distance between the plates) is

Options

  1. A3 2 ε 0 A d
  2. B2 ε 0 A d
  3. C2 3 ε 0 A d
  4. D3 ε 0 A d

Correct answer

C. 2 3 ε 0 A d

Step-by-step solution

From the figure, it is clear that two capacitances will form the equivalent arrangement as shown in figure. Let C be the capacitance of each capacitor. The net capacitance of P and Q connected in parallel C P Q = 2 C Now, C P Q and C are in series. ∴ C X Y = C . C P Q C + C P Q = C . 2 C C + 2 C = 2 3 C The capacitance of parallel plate capacitor C = ε 0 A d ⇒ C X Y = 2 3 ε 0 A d

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