An inductor 20 mH, a capacitor 100 μ F and a resistor 50 Ω are… | NEET 2018

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Power, Power Factor & Wattless Current

An inductor 20 mH, a capacitor 100 $\mu$ F and a resistor 50 $\Omega$ are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is

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Answer: (a)

$\omega = 314$ rad/s: $X_L = 314 \times 0.02 = 6.28\ \Omega$ , $X_C = \frac{1}{314 \times 10^{-4}} = 31.85\ \Omega$ .
$Z^2 = 50^2 + (31.85 - 6.28)^2 = 2500 + 654 = 3154\ \Omega^2$ .
$V_{rms}^2 = \frac{10^2}{2} = 50\text{ V}^2$ .
$P = \frac{V_{rms}^2R}{Z^2} = \frac{50 \times 50}{3154} \approx 0.79\text{ W}$ .
So the answer is (a) 0.79 W.

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