The GATE Grind

GATE 2025 EC – Question 20

Networks, Signals and Systems · Sinusoidal Steady State Analysis · 1 mark · Multiple choice

Let $i_C$, $i_L$, and $i_R$ be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC admittances are given in Siemens (S).

Which one of the following is TRUE?

Diagram for GATE 2025 EC question 20
  1. $i_C=0.25\angle180^\circ$ A, $i_L=0.1\angle0^\circ$ A, $i_R=0.2\angle90^\circ$ A
  2. $i_C=4\angle180^\circ$ A, $i_L=10\angle0^\circ$ A, $i_R=5\angle90^\circ$ A
  3. $i_C=0.25\angle270^\circ$ A, $i_L=0.1\angle90^\circ$ A, $i_R=0.2\angle90^\circ$ A
  4. $i_C=4\angle90^\circ$ A, $i_L=10\angle270^\circ$ A, $i_R=5\angle0^\circ$ A

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $i_C=0.25\angle180^\circ$ A, $i_L=0.1\angle0^\circ$ A, $i_R=0.2\angle90^\circ$ A

Explanation

Each branch current is $I=YV$ with $V=1\angle90^\circ$ V. Capacitor: $j0.25\times1\angle90^\circ=0.25\angle180^\circ$ A. Inductor: $-j0.1\times1\angle90^\circ=0.1\angle0^\circ$ A. Resistor: $0.2\times1\angle90^\circ=0.2\angle90^\circ$ A.