In a series LR circuit, X_{L} = R and power factor of the circuit is P_{1}. When capacitor with capacitance C such that X_{L} = X_{C} is put in series, the power factor becomes P_{2}. Calculate P_{1}/P_{2}

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#### Solution

Given: Power factor *P*_{1} (When X_{L}=R)

New power factor *P _{2} *(When X

_{L}= X

_{C})

`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`

Is there an error in this question or solution?

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