# In a Series Lr Circuit, Xl = R and Power Factor of the Circuit is P1. When Capacitor with Capacitance C Such that Xl = Xc is Put in Series, the Power Factor Becomes P2. Calculate P1/P2 - Physics

In a series LR circuit, XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL = XC is put in series, the power factor becomes P2. Calculate P1/P2

#### Solution

Given: Power factor P1       (When XL=R)
New power factor  P2   (When XL  = XC)

P_1=R/Z

=>P_1=R/sqrt(R^2+X^2)=R/sqrt(2R^2)=1/sqrt2

P_2=R/Z

=>P_2=R/sqrt(R^2+(X_L-X_C)^2)=1

Thus

P_1/P_2=1/sqrt2

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