Question 3.10: In Fig. 3.35 is shown a parallel circuit, an inductance L an......
In Fig. 3.35 is shown a parallel circuit, an inductance L and a parallel R connected across 200 V, 50 Hz ac supply. Calculate:
(a) the current drawn from the supply; (b) apparent power; (c) real power; (d) reactive power.
Resistance of resistive branch, R = 40 Ω
Inductive reactance of inductive branch.
Current drawn by resistive branch, \mathrm{I}_{\mathrm{R}}=\frac{\mathrm{V}}{\mathrm{R}}=\frac{200}{40}=5 \mathrm{~A}
Current drawn by inductive branch, \mathrm{I}_{\mathrm{L}}=\frac{\mathrm{V}}{\mathrm{X}_{\mathrm{L}}}=\frac{200}{20}=10 \mathrm{~A}
(i) Current drawn from the supply (see Fig. 3.36),
\begin{aligned} I & =\sqrt{I_R^2+I_L^2} \\ & =\sqrt{5^2+10^2}=11.18 \mathrm{~A} \end{aligned}(ii) Apparent power, \mathrm{S}=\mathrm{V} \times \mathrm{I}=200 \times 11.18=2.236 \mathrm{kVA}
(iii) Real power, \mathrm{P}=\mathrm{VI} \operatorname{Cos} \phi=\mathrm{VI} \mathrm{I}_{\mathrm{R}}=200 \times 5=1.0 \mathrm{~kW}
(iv) Reactive power, \mathrm{Q}=\mathrm{VI} \operatorname{Sin} \phi=\mathrm{V} \times \mathrm{I}_{\mathrm{L}}=200 \times 10=2.0 \mathrm{kVAR}
