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, $$P=V_{S}I_{S}\cos \phi$$

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

$$I_{S}=22.72A$$

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

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

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

$$\delta =9.209^{\circ}$$