For a series `RLC` circuit `R=X_(L)=2X_(C)`. The impedance of the current and phase different (between) `V` and `i` will be

Options

A. `(sqrt(5)R)/2, tan^(-1)(2)`
B. `(sqrt(5)R)/2, tan^(-1)(1/2)`
C. `sqrt(5) X_(C), tan^(-1)(2)`
D. `sqrt(5) R, tan^(-1)(1/2)`

Answer

B

Explanation

`X_(L)=R, X_(C)=R//2`
`:. tan varphi=(X_(L)-X_(C))/R=(R-R/2)/R=1/2`
`implies varphi=tan^(-1)(1//2)`
Also `Z=sqrt(R^(2)+(X_(L)-X_(C))^(2))=sqrt(R^(2)+(R^(2))/4)=(sqrt(5))/2 R`