An AC circuit has an inductor and a resistor of resistance R in series, such that X L = 3 R . Now, a capacitor is added in series such that X C = 2 R . the ratio of the new power factor with the old power factor of the circuit is 5 : x . The value of x is

Step-by-step solution

First Recall the formula of power factor, cos ϕ = R Z   ⇒ cos ϕ initial   = R Z = R X L 2 + R 2 = R 9 R 2 + R 2 = 1 10 .   ⇒ cos ϕ f i n a l   = R Z = R X L - X C 2 + R 2 = R R 2 + R 2 = 1 2 ⇒ cos ϕ f i n a l   cos ϕ initial   = 5 x ⇒ x = 1