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 p

Question

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

TestHub · Accepted Answer

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

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