In a series LR circuit, X_L=R , power factor is P₁ . If a capacitor of capacitance C with X_C=X_L is added to the circuit the power factor becomes P₂ . The ratio of P₁ to P₂ will be

Step-by-step solution

array ll & Power factor = R R ^2+ X _ L ^2 & Given: X _ L = R & P ₁= R 2 R ^2 = 1 2 array When C is connected, the circuit becomes a series LCR circuit. array ll & Power factor = R R ^2+ ( X _ L - X _ C )^2 & Given: X _ C = X _ L & P ₂= R R ^2 =1 & P ₁: P ₂=1: 2 array