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MHT CET202211 Aug 2022Morning ShiftPhysicsCapacitanceActual

In a parallel plate air capacitor of plate separation d , a dielectric slab of thickness t is introduced between the plates (t < d) . The capacitance becomes one-third of the original value. The dielectric constant of the slab will be

Options

  1. At 2 d+t
  2. Bt d-2 t
  3. Ct d+t
  4. D2 t 2 d-t

Correct answer

A. t 2 d+t

Step-by-step solution

Equivalent Capacitance of the dielectric-air system is given by 1 C^ = ( d-t ₀ A )+ ( t K ₀ A )= d-t (1- 1 K ) ₀ A If new capacitance is given by one third of the old value: aligned & C= ₀ A d-t (1- 1 K ) = ₀ A 3 d & d-t+ t K =3 d & K= t 2 d+t aligned

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