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KCET2007PhysicsCapacitance

A parallel plate capacitor with air as the dielectric has capacitance C . A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be

Options

  1. A(K+3) C 4
  2. B(K+2) C 4
  3. C(K+1) C 4
  4. DK C 4

Correct answer

A. (K+3) C 4

Step-by-step solution

The condenser with air as the dielectric has capacitance C₁= ₀ d ( 3 A 4 )= 3 ₀ A 3 d Similarly, the condenser with K as the dielectric constant has capacitance C₂= ₀ K d ( A 4 )= ₀ A K 4 d Since, C₁ and C₂ are in parallel aligned C_ n e t &=C₁+C₂ &= 3 ₀ A 4 d + ₀ A K 4 d &= ₀ A d [ 3 4 + K 4 ]= C 4 (K+3) aligned

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