GATE EE 2026 Set 1 — Question 25
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Electric Circuits → Network Elements & Sources → Dependent Sources
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Question
Refer to the four circuits shown. Which one of the following options for and makes all of them realizable?
Correct answer
(A) k₁ = 1, k₄ = -1/3, for all values of k₂ and k₃
Solution
Each circuit is a single loop of two sources connected across the same pair of nodes, so the two sources share the same voltage and carry the same loop current. A circuit is realizable only if KVL and KCL can both be satisfied without contradiction.
1.Top left (two voltage sources in parallel): Both sources have at the top, so KVL forces . With , this requires .
2.Top right (voltage source in parallel with a current source): The voltage source fixes the node voltage and the current source fixes the loop current; these do not conflict, so the circuit is realizable for any .
3.Bottom left (current source in parallel with a voltage source): The current source fixes the loop current and the voltage source fixes the voltage across both; again no conflict, so any is allowed.
4.Bottom right (two current sources in parallel): Both arrows point up, so both currents enter the top node. KCL at that node gives , i.e. . With , this requires , so .
Hence all four circuits are realizable exactly when and , with and arbitrary. Options (B), (C) and (D) all have , so the correct choice is option (A).Continue learning with Success Tracker
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