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MHT CET202523 Apr 2025Morning ShiftPhysicsCapacitanceActual

A parallel plate air capacitor has capacity ' C ' and distance of separation between plates is ' d '. If a conducting sheet of thickness 2 ~d 3 is inserted in between the plates, the capacitance becomes C₁ . The ratio of C₁ C is

Options

  1. A2: 1
  2. B4: 1
  3. C3: 1
  4. D5: 1

Correct answer

C. 3: 1

Step-by-step solution

The original capacitance of a parallel plate capacitor is C = ₀ A d . When a conducting sheet of thickness t = 2d 3 is inserted, the electric field only exists in the air gaps. The effective separation becomes d' = d - t = d - 2d 3 = d 3 . The new capacitance is therefore C₁ = ₀ A d' = ₀ A d/3 = 3 ₀ A d . The ratio evaluates to C₁ C = 3 ₀ A d ₀ A d = 3 . Final ratio: 3

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