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Question
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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