Physics Question on Alternating current

Question

In a series $LR$ circuit with $X _{ L }= R$ , power factor is $P _1$ If a capacitor of capacitance $C$ with $X _{ C }= X _{ L }$ is added to the circuit the power factor becomes $P_2$ The ratio of $P_1$ to $P_2$ will be :

Answer 1

Solution

P=ZR⇒P1=R2+XL2R=R2R( as XL=R)
P1=21
P2=R2+(XL−XL)2R=P2=1
P2P1=21