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MHT CET · Physics · Alternating Current

A resistor of \(100 \Omega\), inductor of self inductance \(\left(\frac{4}{\pi^2}\right) \mathrm{H}\) and a capacitor of unknown capacitance are connected in series to an a.c. source of \(200 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. When the current and voltage are in phase, the capacitance and the power dissipated is respectively

  1. A \(2 \times 10^{-5} \mathrm{~F}, 200 \mathrm{~V}\)
  2. B \(3 \times 10^{-5}, 300 \mathrm{~V}\)
  3. C \(4 \times 10^{-5} \mathrm{~F}, 400 \mathrm{~W}\)
  4. D \(2.5 \times 10^{-5} \mathrm{~F}, 400 \mathrm{~W}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2.5 \times 10^{-5} \mathrm{~F}, 400 \mathrm{~W}\)

Step-by-step Solution

Detailed explanation

\(\omega = 2\pi f = 2\pi(50) = 100\pi \mathrm{~rad/s}\) \(C = \frac{1}{\omega^2 L} = \frac{1}{(100\pi)^2 \left(\frac{4}{\pi^2}\right)} = \frac{1}{10000\pi^2 \frac{4}{\pi^2}} = \frac{1}{40000} = 2.5 \times 10^{-5} \mathrm{~F}\)