In the LCR circuit shown (see figure) the current leads the applied voltage. Adding a capacitor C' to the existing capacitor C makes the power factor unity. The capacitor C' must be connected

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(4) in parallel with C, of magnitude (1-ω²LC)/(ω²L). Leading current means the circuit is net capacitive (X_C>X_L); to reach unity power factor we need X_L=X_C,total, i.e. more capacitance. A capacitor in parallel adds: Cₜₒₜₐₗ=C+C'. Resonance needs ω L=1/(ω(C+C')), so C+C'=1/(ω²L). C'=1/(ω²L)-C=(1-ω²LC)/(ω²L), in parallel with C.

In the LCR circuit shown (see figure) the current leads the applied voltage. Adding a capacitor C' to the existing capacitor C makes the power factor unity. The capacitor C' must be connected

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