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MHT CET202616 April 2026Evening ShiftPhysicsCapacitanceActual

A capacitor has capacity C when it's parallel plates are separated by air medium of thickness 'd'. A slab of material of dielectric constant K having area equal to that of plates but thickness d 2 is inserted between the plates. Capacitance of the capacitor in the presence of slab will be

Options

  1. AKC
  2. B2 KC
  3. CKC K +1
  4. D2 KC K +1

Correct answer

D. 2 KC K +1

Step-by-step solution

Initial capacitance of the parallel plate capacitor with air is given by C = ₀ A d When a dielectric slab of thickness t = d 2 and dielectric constant K is inserted, the system can be considered as two capacitors in series. Capacitance of the air-filled part of thickness d 2 is C₁ = ₀ A d 2 = 2 ₀ A d = 2C Capacitance of the dielectric-filled part of thickness d 2 is C₂ = K ₀ A d 2 = 2K ₀ A d = 2KC The equivalent capacitance C' of these two capacitors in series is C' = C₁ C₂ C₁ + C₂ Substituting the values of C₁ and

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