An inductor 20 mH, a capacitor 50 μ F and a resistor 40 Ω are… | NEET 2016 (Phase 1)

Q67NEET 2016 · PHASE 1Medium

Power, Power Factor & Wattless Current

An inductor 20 mH, a capacitor 50 $\mu F$ and a resistor 40 $\Omega$ are connected in series across a source of emf V = 10 sin 340t. The power loss in A.C. circuit is

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Answer: (c)

$\omega = 340$ rad/s: $X_L = 340 \times 0.02 = 6.8\ \Omega$ , $X_C = \frac{1}{340 \times 50 \times 10^{-6}} = 58.8\ \Omega$ .
$Z^2 = 40^2 + (58.8 - 6.8)^2 = 1600 + 2704 = 4304\ \Omega^2$ .
$V_{rms}^2 = \frac{10^2}{2} = 50\text{ V}^2$ .
$P = \frac{V_{rms}^2R}{Z^2} = \frac{50 \times 40}{4304} \approx 0.46\text{ W}$ , closest option 0.51 W.
So the answer is (c) 0.51 W.

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