Answer to Question #143663 in Electric Circuits for Shyam

Question #143663
Three identical coils, each of resistance 10ohm and inductance 42mh are connected in star to a 415v, 50hz, 3 phase supply determine a-phase impedance, b-line voltage, c-phase voltage, d-phase current, power factor, e-power dissipated
1
Expert's answer
2020-11-11T08:56:37-0500

Given are following details,

Resistance /phase(R)=10Ω.(R) =10\varOmega.

Inductance /phase(L)=42mH(L) = 42mH

Hence Inductive reactance(XL)=Lω=42×103×2π×50=13.19Ω.(X_L) =L\omega=42\times10^{-3}\times2\pi\times50=13.19\varOmega.

a) The perphase impedance(Z)=R+jXL=10+j13.19 Ω(Z) =R+jX_L=10+j13.19\space\varOmega


b) Line voltage(VL)=415V(V_L) =415V (given in question)


c) Phase voltage (VP)=VL3=4153=239.6V(V_P) =\frac{V_L}{\sqrt3}=\frac{415}{\sqrt3}=239.6 V


d) Phase current(IP)=VPZ=239.610+j13.19=14.1752.83.A(I_P) =\frac{V_P}{Z}=\frac{239.6}{10+j13.19}=14.17\angle-52.83. A


Powerfactor =cos(52.83)=0.604=\cos(52.83) =0.604


e) Overall power dissipated in the 3phase system =3×IP2×R=3×14.472×10=6281.43W=3\times I_P^2 \times R=3\times14.47^2\times10=6281.43W


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