Question

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

Answer 1

Given are following details,

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

Inductance /phase$(L) = 42mH$

Hence Inductive reactance$(X_L) =L\omega=42\times10^{-3}\times2\pi\times50=13.19\varOmega.$

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

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

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

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

Powerfactor $=\cos(52.83) =0.604$

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