Answer 1

Given: Power factor P₁       (When X_L=R)
            New power factor  P₂   (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`