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(D) For element $X$,the current is in phase with the voltage,so $X$ is a resistor.The resistance $R = \frac{V_0}{I_0} = \frac{100}{5} = 20\,\Omega$.Fo

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$\frac{5}{2}$

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(D) For element $X$,the current is in phase with the voltage,so $X$ is a resistor.The resistance $R = \frac{V_0}{I_0} = \frac{100}{5} = 20\,\Omega$.For element $Y$,the current lags behind the voltage by $\frac{\pi}{2}$,so $Y$ is an inductor.The inductive reactance $X_L = \frac{V_0}{I_0} = \frac{100}{5} = 20\,\Omega$.When $X$ and $Y$ are connected in series,the total impedance $Z = \sqrt{R^2 + X_L^2} = \sqrt{20^2 + 20^2} = 20\sqrt{2}\,\Omega$.The peak current in the series circuit is $I_0 = \frac{V_0}{Z} = \frac{100}{20\sqrt{2}} = \frac{5}{\sqrt{2}}\,A$.The rms current is $I_{rms} = \frac{I_0}{\sqrt{2}} = \frac{5/\sqrt{2}}{\sqrt{2}} = \frac{5}{2}\,A$.

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