b
(b) \({X_L} = R,\;\;{X_C} = R/2\)

\(\therefore \tan \phi = \frac{{{X_L} - {X_C}}}{R} = \frac{{R - \frac{R}{2}}}{R} = \frac{1}{2}\)

\( \Rightarrow \phi = {\tan ^{ - 1}}(1/2)\)

Also\(Z = \sqrt {{R^2} + {{({X_L} - {X_C})}^2}} = \sqrt {{R^2} + \frac{{{R^2}}}{4}} = \frac{{\sqrt 5 }}{2}R\)