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MHT CET202521 Apr 2025Evening ShiftPhysicsCapacitanceActual

If the charge on the capacitor is increased by 3 C , the energy stored in it increases by 21 % . The original charge on the capacitor is

Options

  1. A6 C
  2. B3 C
  3. C30 C
  4. D90 C

Correct answer

C. 30 C

Step-by-step solution

The energy stored in a capacitor with charge Q is U = Q^2 2C . Increasing the charge by 3 C yields Q' = Q + 3 , with new energy U' = (Q+3)^2 2C . Given that energy increases by 21 % , we have U' = 1.21U : (Q+3)^2 2C = 1.21 Q^2 2C . Canceling the common factor 1 2C yields: (Q+3)^2 = 1.21Q^2 . Taking square roots: Q+3 = 1.1Q , since quantities are positive. Solving for Q : 3 = 0.1Q , therefore Q = 30 C . Final Answer: C. 30 C

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