In series `LR` circuit, `X_(L) = 3 R`. Now a capacitor with `X_(C ) = R` is added in series. The ratio of new to old power factor

Options

A. `sqrt2`
B. `(1)/(sqrt2)`
C. 2
D. 1

Answer

A

Explanation

In series `LR` circuit,
Power factor, `cos phi_(1) = (R )/(Z)`
`= (R )/(sqrt(R^(2) +X_(L)^(2))) = (R )/(sqrt(R^(2) + 9 R^(2))`
` = (R )/(R sqrt(10)) = (1)/(sqrt10)`
When capacitor with `X_(C ) = R` is added in series, new power factor,
`phi_(2) = (R )/(Z) = (R )/(sqrt(R^(2) + (X_(L) - X_(C ))^(2)))`
`cos phi_(2) = (R )/(sqrt(R^(2) + (3 R - R)^(2))) = (R )/(R sqrt5)`
`:. (cos phi_(2))/(cos phi_(1)) = (1)/(sqrt5) sqrt(10)/(1) = sqrt2`