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CUET · PHYSICS · PYQ PAPER 2025

For the L-R series circuit connected to an ac mains \(e = e_0 \sin \omega t\), the average power consumed is: (Symbols have their usual meanings)

  1. A \(\frac{e_0^2 R}{2(R^2 + \omega^2 L^2)}\)
  2. B \(\frac{e_0^2 L}{2\left(R^2+\omega^2 L^2\right)}\)
  3. C \(\frac{e_0^2}{2(R^2 + \omega^2 L^2)}\)
  4. D \(\frac{e_0^2}{2(R^2 + \omega^2 R^2)}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{e_0^2 R}{2(R^2 + \omega^2 L^2)}\)

Step-by-step Solution

Detailed explanation

\(P_{avg} = I_{rms}^2 R\) \(I_{rms} = \frac{e_0/\sqrt{2}}{Z}\) \(Z = \sqrt{R^2 + (\omega L)^2}\) \(P_{avg} = \left(\frac{e_0/\sqrt{2}}{\sqrt{R^2 + (\omega L)^2}}\right)^2 R\) \(P_{avg} = \frac{e_0^2}{2(R^2 + \omega^2 L^2)} R\) \(P_{avg} = \frac{e_0^2 R}{2(R^2 + \omega^2 L^2)}\)
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