An AC source is connected to an inductance of 100 mH, a capacitance… | JEE Main 2022 (28 Jun, Shift 1)

Q55JEE Main 2022 · 28 JUN · SHIFT 1Difficult

Power, Power Factor & Wattless Current

An AC source is connected to an inductance of 100 mH, a capacitance of 100 $\mu$ F and a resistance of 120 $\Omega$ as shown in figure. The time in which the resistance having a thermal capacity 2 J/ $^\circ$ C will get heated by 16 $^\circ$ C is _____________ s.

Numerical answer type. Work it out, then open the answer.

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Answer: 15

$\omega = 100$ : $X_L = 10\ \Omega$ , $X_C = \frac{1}{100\times 10^{-4}} = 100\ \Omega$
$Z = \sqrt{120^2 + 90^2} = 150\ \Omega$ , $V_{rms} = 20$ V, $I = \frac{20}{150} = \frac{2}{15}$ A
$P = I^2R = \frac{4}{225}\times 120 = \frac{32}{15}$ W
Heat needed $= 2\times 16 = 32$ J, $t = 32 \div \frac{32}{15} = 15$ s

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