A series LCR circuit is connected to an AC source. When L alone is removed, current and applied voltage differ in phase by π/3. When C alone is removed, the phase difference is also π/3. What is the power factor of the full LCR circuit?
Options

Question

A series LCR circuit is connected to an AC source. When L alone is removed, current and applied voltage differ in phase by π/3. When C alone is removed, the phase difference is also π/3. What is the power factor of the full LCR circuit?

Options

G1 Physics · Accepted Answer

Step 1: With L removed, the series RC phase angle has tanφ=X_C/R and φ=π/3, so X_C=√3R. Step 2: With C removed, the series RL angle similarly has X_L/R=tan(π/3)=√3, so X_L=√3R. Step 3: In complete LCR circuit, reactances cancel: X_L−X_C=0. Step 4: Power factor cosφ=R/√[R²+(X_L−X_C)²]=1. Final answer: (B) 1.0.