The GATE Grind

GATE 2022 EE – Question 34

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 1 mark · Numerical answer

Two balanced three-phase loads, as shown in the figure, are connected to a $100\sqrt3$ V, three-phase, 50 Hz main supply. Given $Z_1=(18+j24)\ \Omega$ and $Z_2=(6+j8)\ \Omega$. The ammeter reading, in amperes, is ________. (round off to nearest integer)

Diagram for GATE 2022 EE question 34

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 20

Explanation

The delta-connected $Z_1$ is equivalent to a star of $\frac{Z_1}{3}=6+j8\ \Omega$. In parallel with the star-connected $Z_2=6+j8\ \Omega$ this gives $3+j4=5\angle53.1^\circ\ \Omega$ per phase. The phase voltage is $\frac{100\sqrt3}{\sqrt3}=100$ V, so the line current is $\frac{100}{5}=20$ A.