As shown in the figure an inductor of inductance \( 200 \, \text{mH} \) is connected to an AC source of emf \( 220 \, \text{V} \) and frequency \( 50 \, \text{Hz} \). The instantaneous voltage of the source is \( 0 \, \text{V} \) when the peak value of current is \( \frac{\sqrt{a}}{\pi} \, \text{A} \). The value of \( a \) is ________.
