In the circuit shown, an ideal switch $S$ is operated at $100$ kHz with a duty ratio of $50 \%$. Given that $\Delta i_c$ is $1.6$ A peak-to-peak and $I_0$ is $5$ A dc, the peak current in $S$ is
1. $6.6$ A
2. $5.0$ A
3. $5.8$ A
4. $4.2$ A