1. Identify element $X$

Since the current is in phase with voltage, element $X$ is a pure resistor.

Given peak voltage and peak current: $V_0 = 100\text{ V}, \qquad I_0 = 5\text{ A}$

So its resistance is $R = \frac{V_0}{I_0} = \frac{100}{5} = 20\,\Omega$

2. Identify element $Y$

The current lags the voltage by $\frac{\pi}{2}$, so $Y$ is a pure inductor.

Its inductive reactance is $X_L = \frac{V_0}{I_0} = \frac{100}{5} = 20\,\Omega$

3. Connect $X$ and $Y$ in series

Now the circuit is a series combination of resistance $R=20\,\Omega$ and inductive reactance $X_L=20\,\Omega$.

Hence the impedance is $Z = \sqrt{R^2 + X_L^2} = \sqrt{20^2 + 20^2} = 20\sqrt{2}\,\Omega$

4. Find peak current in series combination

Using $I_0 = \frac{V_0}{Z} = \frac{100}{20\sqrt{2}} = \frac{5}{\sqrt{2}}\text{ A}$

5. Find rms current

For sinusoidal current, $I_{\text{rms}} = \frac{I_0}{\sqrt{2}} = \frac{5/\sqrt{2}}{\sqrt{2}} = \frac{5}{2}\text{ A}$

6. Check options

$\boxed{\frac{5}{2}\text{ A}}$

So the correct option is D.