A 750 Hz, 20 V (rms) source is connected to a resistance of 100 Ω, an… | JEE Main 2020 (3 Sep, Shift 1)

Q61JEE Main 2020 · 3 SEP · SHIFT 1Difficult

Power, Power Factor & Wattless Current

A 750 Hz, 20 V (rms) source is connected to a resistance of 100 $\Omega$ , an inductance of 0.1803 H and a capacitance of 10 $\mu$ F all in series. The time in which the resistance (heat capacity 2 J/oC) will get heated by 10oC. (assume no loss of heat to the surroudnings) is close to:

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Answer: (a)

$\omega = 2\pi\times 750 \approx 4712$ rad/s
$X_L = 4712\times 0.1803 \approx 849.6\ \Omega$ , $X_C = \frac{1}{4712\times 10^{-5}} \approx 21.2\ \Omega$
$Z = \sqrt{100^2 + 828.4^2} \approx 834.4\ \Omega$ , $I = 20/834.4 \approx 0.024$ A
$P = I^2 R \approx 0.0574$ W; heat needed $= 2\times 10 = 20$ J
$t = 20/0.0574 \approx 348$ s, so the answer is (a).

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