d
(d) \(Z = \sqrt {{{(R)}^2} + {{({X_L} - {X_C})}^2};} \)

\(R = 10\,\Omega ,\,\,{X_L} = \omega L = 2000 \times 5 \times {10^{ - 3}} = 10\,\Omega \)

\({X_C} = \frac{1}{{\omega C}} = \frac{1}{{2000 \times 50 \times {{10}^{ - 6}}}} = 10\,\Omega \,\,i.e.\,Z = 10\,\Omega \)

Maximum current \({i_0} = \frac{{{V_0}}}{Z} = \frac{{20}}{{10}} = 2A\)

Hence \({i_{rms}} = \frac{2}{{\sqrt 2 }} = 1.4\,A\) and \({V_{rms}} = 4 \times 1.41 = \,\) \(5.64\,\,V\)