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MHT CET202527 Apr 2025Evening ShiftPhysicsCapacitanceActual

If the charge on the capacitor is increased by 2C, the energy stored in it increases by 21 % . The original charge on the capacitor is

Options

  1. A20 C
  2. B15 C
  3. C10 C
  4. D5 C

Correct answer

A. 20 C

Step-by-step solution

The original charge Q and capacitance C yield stored energy U = Q^2 2C . After adding 2 C , the charge becomes Q + 2 and energy becomes U' = (Q + 2)^2 2C . Given a 21 % energy increase, U' = 1.21U , so [ (Q + 2)^2 2C = 1.21 Q^2 2C . ] Canceling 1 2C from both sides, (Q + 2)^2 = 1.21Q^2 . Solving this quadratic equation gives Q + 2 = 1.1Q . The positive case yields Q = 2 0.1 = 20 C , while the negative case gives Q = - 2 2.1 C , which is discarded. Final answer: 20 C

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