The GATE Grind

GATE 2026 EE – Question 25

Electric Circuits · Network Elements: Ideal voltage and current sources, dependent sources, R, L, C, M elements · 1 mark · Multiple choice

Refer to the four circuits shown.

Which one of the following options for $k_1$, $k_2$, $k_3$, and $k_4$ makes all of them realizable?

Diagram for GATE 2026 EE question 25
  1. $k_1=1,\ k_4=-1/3$, for all values of $k_2$ and $k_3$
  2. $k_2=-2,\ k_3=+1/3$, for all values of $k_1$ and $k_4$
  3. $k_1=2,\ k_2=0.5,\ k_3=-2/3,\ k_4=-3$
  4. $k_1=2,\ k_2=-0.5,\ k_3=-2/3,\ k_4=+3$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $k_1=1,\ k_4=-1/3$, for all values of $k_2$ and $k_3$

Explanation

Circuit 1 has two ideal voltage sources directly in parallel, which is only consistent if they have the same value: $k_1V_D=V_D$, so $k_1=1$. Circuit 2 has a current source across a voltage source and Circuit 3 has a voltage source in series with a current source, so both are realizable for any $k_2$ and $k_3$. Circuit 4 has two ideal current sources in series but pointing in opposing directions around the loop, which requires $3k_4I_D=-I_D$, i.e. $k_4=-1/3$.