Gate 2016 EE -Set 2 - Question 48

Given, V=400V, P=5kW, V_{s}=220V(rms), f=50Hz, \cos \phi =1, L=5mH, \delta =?

The power formula is, P=V_{S}I_{S}\cos \phi

\Rightarrow 5\times 10^{3}=220I_{S}\times 1

I_{S}=22.72A

\tan \delta =\frac{I_{S}X_{S}}{V_{S}}

\delta =\tan ^{-1}\frac{I_{S}(2\pi fL)}{V_{S}}

\delta =\tan ^{-1}\frac{22.72\times 2\times 3.14\times 50\times 5\times 10^{-3}}{220}

\delta =9.209^{\circ}