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Two impedances of 12+j16 Ω and 10-J20Ω are connected in parallel across 230V, 50Hz, 1Ω, ac supply. Find the kW, kVA, kVAR and power factor of each branch.
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ˉZ=12+j16ΩˉZ=10j20ΩV=230 V

Let  ˉV=230<0V

ˉI1=ˉVˉZ1=230<012+j16=11.5<53.13 A

ˉI2=ˉVˉZ2=230<010j20=10.29<63.43 A

(i) kW, kVA, kVAR and power factor of branch 1

P1=VI1cosϕ1=230×11.5×cos(53.13)=1.59 kWS1=VI1=230×11.5=2.65 kVAQ1=VI1sinϕ1=230×11.5×sin(53.13)=2.12 kVARpf1=cosϕ1=cos(53.13)=0.6 (lagging)

 

(ii) kW, kVA, kVAR, and power factor of branch 2

P2=VI2cos ϕ2=230×10.29×cos(63.43)=1.06 kWS2=VI2=230×10.29=2.37 kVAQ2=VI2sinϕ2=230×10.29×sin(63.43)=2.12 kVARpf2=cosϕ2=cos(63.43)=0.447 (leading)

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