GATE EE 2026 Set 1 — Question 24
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Electric Circuits → Network Theorems → Thevenin's Theorem
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Question
For the circuit shown, which one of the following options correctly identifies the Thevenin’s equivalent parameters between nodes Y and Z?
Correct answer
(B) V_(TH) = 140 V, R_(TH) = 0 Ω
Solution
To find the Thevenin equivalent parameters between nodes Y and Z, we calculate the open-circuit voltage () and the equivalent resistance () with sources deactivated.1. Finding :
We need to find the voltage difference . Let node W be the reference node ().
To find , we deactivate all independent sources. Ideal voltage sources are replaced by short circuits.
We need to find the voltage difference . Let node W be the reference node ().
- From the source between X and W, .
- From the source between X and Y (with the positive terminal at Y), .
- From the source between Z and W (with the positive terminal at W), .
- Therefore, .
To find , we deactivate all independent sources. Ideal voltage sources are replaced by short circuits.
- Shorting the source between X and Y creates a short between nodes X and Y.
- Shorting the source between X and W creates a short between nodes X and W.
- Shorting the source between Z and W creates a short between nodes Z and W.
- Consequently, there is a continuous short-circuit path from node Y to node Z (Y X W Z). Any resistors in parallel with this path are bypassed.
- Thus, the equivalent resistance between Y and Z is .
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