Answer to Question #92880 in Electric Circuits for BHARAT BHUSHAN KAUNDAL

Question #92880
A balanced delta connected load takes 20 KVA at 0.8 power factor when connected to a 415 v, 3 sigma system.Calculate the resistance of each branch of balanced star connected non reactive load which when connected to same supply coil takes the same power?
1
Expert's answer
2019-08-22T09:23:51-0400

The active power per each phase (since the load is balanced, it means that all branches have the same impedance) can be calculated as


P=S cosϕ3.P=\frac{S\space\text{cos}\phi}{\sqrt{3}}.

With non-reactive load each phase of the star-connected load has power of


P=Uphase2Rbranch,P=\frac{U^2_\text{phase}}{R_\text{branch}},

and therefore


Rbranch=Uphase2P=3Uphase2S cosϕ=3[Uline2/3]S cosϕ,R_\text{branch}=\frac{U^2_\text{phase}}{P}=\frac{\sqrt{3}\cdot U^2_\text{phase}}{S\space\text{cos}\phi}=\frac{\sqrt{3}\cdot [U^2_\text{line}/3]}{S\space\text{cos}\phi},

Rbranch=34152/3200000.8=6.21 Ω.R_\text{branch}=\frac{\sqrt{3}\cdot 415^2/3}{20000\cdot0.8}=6.21\space\Omega.


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