Question

An electrical load operates at 240 V rms The load absorbs an average of 8 Kw at lagging power factor of 0.9 The load impedance is:

 Select one:

 A 5.04 L 45 57 °Ω

 B 3.6 L 60 °Ω

 C 5.76 L 36.87 °Ω

 D 4.32 L 53.13 °Ω

 E 6.48 L 25.84 °Ω

Answer 1

Average power, P $= 8KW$

But $P=/S/ cos \theta$

Given power factor $cos \theta=0.9$

$=sin \theta=\sqrt{1-cos^2\theta}$

$=sin \theta=\sqrt{1-0.9^2}=\sqrt{0.19}=0.44$

$P=/S/ cos \theta$

$8KW=/S/*0.9$

$/S/=\frac{8000}{0.9}=8888.89$

Reactive power, Q $=/S/ sin\theta$ VAR

$Q=8888.89(0.44)=3910.72$ VAR

$S=P+jQ$

$S=8000+j3910.72$

$S=8+j3.91$ KVA

Impedence, Z $\frac{S}{I^2}=4.32 \angle 53.13 °Ω$