Three similar coils, connected in star, take a total power of 1.5 kW at a p.f. of 0.2 lagging from a three phase, 440 V, 50 Hz Supply. Calculate the resistance and inductance of each coil.

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written 3.9 years ago by

teamques10 ★ 69k

• modified 3.9 years ago

analog electronics

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written 3.9 years ago by

teamques10 ★ 69k

$P=\sqrt{3 } V_L I_L cos⁡ϕ\\[2ex] 1500=\sqrt{3}\times440\times I_L\times0.2\\[2ex] I_L=9.84 \ A$

For Star load,

$I_{ph}=I_L\\[2ex] I_{ph}=9.84 \ A$

$Z_ph=\dfrac{V_{ph}}{I_{ph}} =\frac{(V_L\sqrt{3})}{I_{ph}} =\dfrac{(440\sqrt{3})}9.84=25.82 \ Ω\\[2ex] cos⁡ϕ=\dfrac{R_{ph}}{Z_{ph}} \\[2ex] R_{ph}=25.82\times0.2=5.164 \ Ω\\[2ex] cos \ ⁡ϕ=0.2$

So,

$ϕ=cos^{-1}⁡0.2=78.46^{\circ}\\[2ex] X_{ph}=Z_{ph}\times sin⁡\ ϕ=25.82 sin⁡(78.46^{\circ})=25.3 \ Ω\\[2ex] L_{ph}=\dfrac{X_{ph}}{2πf=25.3}(2\times3.14\times50)=80.53mH$

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