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JEE MainPhysicsCapacitance

A parallel plate capacitor has a plate separation d . When a metal sheet of thickness t is introduced parallel to the plates, the capacitance of the system increases by 25 % . The thickness t of the metal sheet is:

Options

  1. Ad 4
  2. B4d 5
  3. Cd 5
  4. D5d 4

Correct answer

C. d 5

Step-by-step solution

The initial capacitance of the parallel plate capacitor is C = ₀ A d . When a metal sheet of thickness t is inserted, the new capacitance is C' = ₀ A d - t . It is given that the capacitance increases by 25 % , so the new capacitance is: C' = C + 0.25C = 1.25C = 5 4 C Substituting the expressions for C and C' : ₀ A d - t = 5 4 ( ₀ A d ) 1 d - t = 5 4d 5(d - t) = 4d 5d - 5t = 4d 5t = d t = d 5 Answer: d 5

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