In a series L R circuit X L = R and power factor of the circuit is P 1 . When capacitor with capacitance C such that X L = X C is put in series, the power factor becomes P 2 . The ratio P 1 P 2 is

Step-by-step solution

In case of L - R circuit Z = X L 2 + R 2 Therefore, power factor P 1 = cos ϕ = R Z As X L = R ⇒ Z = 2 R ⇒ P 1 = R 2 R ⇒ P 1 = 1 2 In case of L - C - R circuit Z = R 2 + X L - X C 2 According to the question X L = X C ⇒ Z = R ⇒ P 2 = cos ϕ = R R = 1 ⇒ P 1 P 2 = 1 2