A balanced 3-φ, star connected load consists of three coils each consisting of R = 6 Ω and XL = 8 Ω. Determine the 1) phase impedance 2) phase voltage 3) phase current 4) line current 5) power factor when connected across a 400 V, 50 Hz supply. (aske…

Answer: \(Z_{ph}=10\ \Omega\), \(V_{ph}=230.94\) V, \(I_{ph}=I_L=23.09\) A, pf \(=0.6\) lagging (total power 9.6 kW).

Star connection: \(V_L=\sqrt3V_{ph}\), \(I_L=I_{ph}\).

1) \(Z_{ph}=\sqrt{R^2+X_L^2}=\sqrt{6^2+8^2}=10\ \Omega\) \((=10\angle53.13^\circ)\).

2) \(V_{ph}=\dfrac{V_L}{\sqrt3}=\dfrac{400}{\sqrt3}=230.94\) V.

3) \(I_{ph}=\dfrac{V_{ph}}{Z_{ph}}=\dfrac{230.94}{10}=23.09\) A.

4) \(I_L=I_{ph}=23.09\) A.

5) \(\cos\phi=\dfrac{R}{Z_{ph}}=\dfrac6{10}=0.6\) lagging.

Extra: \(P=\sqrt3V_LI_L\cos\phi=\sqrt3\times400\times23.09\times0.6=9600\) W \(=3I_{ph}^2R\) ✓; \(Q=12.8\) kVAR; \(S=16\) kVA.