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MHT CET20226 Aug 2022Evening ShiftPhysicsCapacitanceActual

A parallel plate air filled capacitor of capacitance C has plate area A and the distance between the plates d . When a metal sheet of thickness ( d 2 ) and of the same area A is introduced between the plates, its capacitance becomes C₂ . The ratio C₂: C₁ is

Options

  1. A4: 1
  2. B2: 1
  3. C3:1
  4. D3: 2

Correct answer

B. 2: 1

Step-by-step solution

The capacitance of the air filled parallel plate capacitor is given by When a slab of dielectric constant K , and thickness t is introduced in between the plates of the capacitor, its new capacitance is given by C^ . This leads to parallel combination of two capacitors: 1 C^ = d-t ₀ A + t K ₀ A = d+t ( 1 K -1 ) ₀ A Since a metal sheet of thickness d / 2 is introduced, hence here, t=d / 2 , K= (for metals) or 1 K =0 Taking ratio of equation (2) and (1), C^ C = 2 ₀ A d ₀ A d = 2 1 =2: 1

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