In the circuit shown, the n : 1 step-down transformer and the diodes are ideal. The diodes have no voltage drop in forward biased condition. If the input voltage (in Volts) is $V_s(t) = 10 \sin\omega t$ and the average value of load voltage $V_L(t)$ (in Volts) is $\frac{2.5}{\pi}$, the value of n is _____.

As shown in the circuit, the initial voltage across the capacitor is 10 V, with the switch being open. The switch is then closed at $t = 0$. The total energy dissipated in the ideal Zener diode $(V_Z = 5 ext{ V})$ after the switch is closed (in mJ, rounded off to three decimal places) is _________.