Three similar coils, connected in stars, take a total power of 18kw of power factor of 0.866 logging from a 3 phase 400 volts, 50Hz system. Calculate the resistance and inductance of each coil. Also draw the pharos drawing showing the current and voltages. -

Given

$P_{ACTIVE}=18kw, \\ \; \cos \emptyset=0.866 \\ \; V_L=400V$

In Star connection

$e_{ph}=\dfrac{V_L}{\sqrt3}=230.94 V \\ \; P_{ACTIVE}=\sqrt3V_LI_L \cos \emptyset$

$I_L$ $=\dfrac{18\times1000}{\sqrt3\times400\times0.866} \\ \; =\dfrac{180}{6} \\ \; =30A$

$\cos \emptyset=\dfrac RZ= \gt R=Z \cos \emptyset=6.666\Omega \\ \; X_L=\sqrt{Z^2-R^2}=3.85\Omega \\ \; L=\dfrac{X_L}{2\pi f}=\dfrac{3.85}{100 \times \pi}=0.01226 H \\ \; R=6.666 \Omega \\ \; L=0.01226 H$

$V_{ph}=230.94 V \\ \; I_{ph}=30 A$

$V_L=400V \\ \; \emptyset=30^0$ $\hspace{2cm}$ $Scale:-for100V=1cm \\ \; \text{for current}10A=1cm$