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99 Percentile Qs Bank for JEE MainPhysicsCapacitance

A parallel plate capacitor with air as a dielectric has capacitance C . A slab of dielectric constant K , having 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. AK + 3 C 4
  2. BK + 2 C 4
  3. CK + 1 C 4
  4. DK C 4

Correct answer

A. K + 3 C 4

Step-by-step solution

The two condensers with K and with air are in parallel. With air, C 1 = ε 0 d 3 A 4 = 3 ε 0 A 4 d With medium, C 2 = ε 0 K d A 4 = ε 0 A K 4 d ∴ C ′ = C 1 + C 2 or C ′ = 3 ε 0 A 4 d + ε 0 A K 4 d = ε 0 A d 3 4 + K 4 or C ′ = C 4 K + 3 ∵ C = A ε 0 d

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