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JEE Main 2023 (30 Jan, Shift 1) · Power, Power Factor & Wattless Current

Power, Power Factor & Wattless Current question from JEE Main 2023 (30 Jan, Shift 1)

Q50JEE Main 2023 · 30 JAN · SHIFT 1Medium

Power, Power Factor & Wattless Current

In a series LR circuit with $X_L = R$ , power factor P1. If a capacitor of capacitance C with $X_C = X_L$ is added to the circuit the power factor becomes P2. The ratio of P1 to P2 will be:

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Answer: (a)

$X_L=R$ : $Z=\sqrt{2}R$ , $P_1 = R/Z = 1/\sqrt{2}$ .
With $X_C = X_L$ the circuit is at resonance: $Z=R$ , $P_2=1$ .
$P_1:P_2 = 1:\sqrt{2}$ , so the answer is (a).

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