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MHT CET2017PhysicsCapacitance

Two parallel plate air capacitors of the same capacity C are connected in series to a battery of emf E . Then one of the capacitors is completely filled with the dielectric material of constant K . The change in the effective capacitance of the series combination is

Options

  1. AC 2 K - 1 K + 1
  2. BC 4 K - 1 K + 1
  3. CC 2 K + 1 K - 1
  4. DC 2 K - 1 K + 1 2

Correct answer

A. C 2 K - 1 K + 1

Step-by-step solution

1 C 1 = 1 C + 1 C = 2 C ⇒ C 1 = C 2 1 C 2 = 1 C + 1 K C 1 C 2 = 1 C 1 + 1 K ∴ C 2 = C 1 + 1 K = C K ( K + 1 ) ∆ C = C K ( K + 1 ) - C 2 = C K K + 1 - 1 2 = C 2 K - K - 1 2 ( K + 1 ) = C 2 K - 1 K + 1

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