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MHT CET 2023 (10 May, Shift 1) · Power, Power Factor & Wattless Current

Power, Power Factor & Wattless Current question from MHT CET 2023 (10 May, Shift 1)

Q49MHT CET 2023 · 10 MAY · SHIFT 1Medium

Power, Power Factor & Wattless Current

In a series LR circuit, $X_L = R$ , power factor is $P_1$ . If a capacitor of capacitance $C$ with $X_C = X_L$ is added to the circuit the power factor becomes $P_2$ . The ratio of $P_1$ to $P_2$ will be

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Answer: (b)

Power factor $\cos\phi = R/Z$ .
LR with $X_L=R$ : $Z=\sqrt{2}R \Rightarrow P_1 = 1/\sqrt{2}$ .
Adding C with $X_C=X_L$ gives resonance: $Z=R \Rightarrow P_2=1$ .
$P_1:P_2 = 1:\sqrt{2}$ , so the answer is (b).

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