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MHT CET202521 Apr 2025Evening ShiftPhysicsAlternating CurrentActual

An alternating e.m.f. having voltage V=V₀ t is applied to a series L-C-R circuit. Given : |X_L-X_C |=R . The r.m.s. value of potential difference across capacitor will be

Options

  1. AV₀ R C
  2. BV₀ R C
  3. CV₀ 2 R C
  4. DV₀ 2 R C

Correct answer

C. V₀ 2 R C

Step-by-step solution

The peak voltage V₀ has r.m.s. value V_ rms = V₀/ 2 . Given |X_L - X_C| = R , the circuit impedance becomes Z = R^2 + R^2 = R 2 . The r.m.s. current is I_ rms = V_ rms /Z = (V₀/ 2 )/(R 2 ) = V₀/(2R) . The r.m.s. voltage across the capacitor is V_ C, rms = I_ rms X_C = (V₀/(2R))(1/ C) . Final answer: V₀ 2R C

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