In a series L R circuit with 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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In case of L R circuit: Given: X L = R P 1 = cos ϕ = R Z = R R 2 + X L 2 = 1 2 In case of L C R circuit: P 2 = cos ϕ = R Z = R R 2 + X L - X C 2 = 1 Therefore, P 1 P 2 = 1 : 2

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