1)

For a series RLC circuit R = XL =  2Xc. The impedance of the circuit and phase difference between V and I respectively will be

A) $\frac{\sqrt{5}r}{2}$, $\tan^{-1}$(2)

B) $\frac{\sqrt{5}r}{2}$, $\tan^{-1}$ $\frac{1}{2}$

C) $\sqrt{5X_{c}}$, $\tan^{-1}$(2)

D) $\sqrt{5R}$, $\tan^{-1}$ $\frac{1}{2}$

Option B

### Explanation:

Given R= XL = 2XC

Z = $\sqrt{R^{2} + (X_{L}-X_{C})^2}$

= $\sqrt{(2X_{C})^2 + (2X_{C}-X_{C})^2}$

= $\sqrt{4X_C^2+X_C^2}$

= $\sqrt{5X_{c}}$ = $\frac{\sqrt{5R}}{2}$

['.'R = 2XC]

$\tan\phi = \frac{X_{L} - X_{C}}{R}$

= $\frac{2X_{C} - X_{C}}{2X_{C}}$

$\tan\phi = \frac{1}{2}$ ; $\phi = \tan^{-1}(\frac{1}{2})$