In a series LR circuit Xₗ=3R. A capacitor with X꜀=R is added in series. The ratio of the new power factor to the old power factor is:
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In a series LR circuit Xₗ=3R. A capacitor with X꜀=R is added in series. The ratio of the new power factor to the old power factor is:

G1 Physics · Accepted Answer

Initially cosφ₁=R/√(R²+9R²)=1/√10. After adding the capacitor, net reactance=2R, so cosφ₂=1/√5. Therefore cosφ₂/cosφ₁=√2.