In a series LR circuit with X(L) = R, power factor is P₁. If a capacitor of capacitance C with X(C) = X(L) is added to the circuit the power factor becomes P₂. The ratio P₁ to P₂ will be:
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Question

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

G1 Physics · Accepted Answer

Initially Z = √(R² + X(L)²) = R√2, so P₁ = R/Z = 1/√2. After adding the capacitor with X(C)=X(L), net reactance becomes zero and P₂ = 1. Hence P₁:P₂ = 1:√2.