A resistor of resistance R and an inductor of inductive reactance R are connected in series to an ac source. A capacitor of capacitive reactance 2 R is then connected in series with L and R . The ratio of the power fators of L R and LCR circuits is

Step-by-step solution

Power factor of LCR circuit is aligned P ₁= & = R R ^2+ ( X _ L - X _ C )^2 = R R ^2+(2 R - R )^2 & = 1 2 aligned Power factor of L R circuit is aligned & P ₂= R R ^2+ X _ L ^2 = R R ^2+ R ^2 = 1 2 & Ratio = P ₂ P ₁ = 1 1 aligned