The GATE Grind

GATE 2015 EC – Question 18

Networks, Signals and Systems · Circuit Analysis · 1 mark · Multiple choice

In the given circuit, the values of $V_1$ and $V_2$ respectively are

A 5 A current source feeds, through a $4\ \Omega$ resistor, a node with three parallel branches to ground: a $4\ \Omega$ resistor carrying current $I$, another $4\ \Omega$ resistor, and a dependent current source $2I$. $V_1$ is the voltage at this node and $V_2$ is the voltage across the 5 A source.
  1. 5 V, 25 V
  2. 10 V, 30 V
  3. 15 V, 35 V
  4. 0 V, 20 V

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 5 V, 25 V

Explanation

Let the node voltage be $V_1$. The resistor with current $I$ has $I = \frac{V_1}{4}$, and the other $4\ \Omega$ resistor carries the same current. KCL at the node: $5 = I + I + 2I = 4I$, so $I = 1.25$ A and $V_1 = 5$ V. The series $4\ \Omega$ resistor carries 5 A, dropping 20 V, so $V_2 = 20 + 5 = 25$ V.