GATE Electrical Engineering (EE) 2018 Solved Paper

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 ${\mathit{V}}_0=\frac{{\mathit{V}}_{\mathit{m}}}{2\mathit{\pi }}\left(3+\cos \mathit{\alpha }\right)$, where ${\mathit{V}}_{\mathit{m}}=80\mathit{\pi }$ volts and $\mathit{\alpha }$ is the firing angle. If the power delivered to the lossless batter is $1600\mathit{W}$. $\mathit{\alpha }$ in degree is ___________(upto 2 decimal places).