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A phase controlled single phase rectifier, supplied by an AC source, feeds power to an $R-L-E$ load as shown in the figure. The rectifier output voltage has an average value given by $V_{\text{o}}= \frac{V_m}{2 \pi} (3+\cos \alpha)$, where $V_m = 80 \pi$ volts and $\alpha$ is the firing angle. If the power delivered to the lossless battery is $1600$ W, $\alpha$ in degree is ___________ (up to $2$ decimal places).

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