The figure below shows a half-bridge voltage source inverter supplying an RL-load with $R=40 \Omega$ and $L=(\frac{0.3}{\pi})H$. The desired fundamental frequency of the load voltage is $50$Hz. The switch control signals of the converter are generated using sinusoidal pulse width modulation with modulation index. $M=0.6$. At $50$Hz, the RL-load draws an active power of $1.44$kW. The value of $DC$ source voltage $V_{DC}$ in volts is.
- $300\sqrt{2}$
- $500$
- $500\sqrt{2}$
- $1000\sqrt{2}$