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MHT CET202618 April 2026Morning ShiftPhysicsCapacitanceActual

Two circular plates each of radius ' r ' are kept parallel to each other distance ' d ' apart. The capacitance of the capacitor formed is ' C₁ '. If the radius of each of the plates is increased to 3 times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes ' C₂ '. The ratio C₁ : C₂ is

Options

  1. A1 : 2
  2. B1 : 4
  3. C1 : 6
  4. D6 : 1

Correct answer

C. 1 : 6

Step-by-step solution

The capacitance of a parallel plate capacitor is given by C = ₀ A d For circular plates of radius r , the area is A = r^2 Initial capacitance is C₁ = ₀ r^2 d When the radius is increased to 3 r , the new area is A' = ( 3 r)^2 = 3 r^2 The new distance of separation is d' = d 2 The new capacitance is C₂ = ₀ (3 r^2) d/2 = 6 ₀ r^2 d Taking the ratio of C₁ and C₂ : C₁ C₂ = ₀ r^2 d 6 ₀ r^2 d = 1 6 The ratio C₁ : C₂ is 1 : 6 Answer: 1 : 6

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