GATE 2023 IN Q.31: solution and answer

GATE 2023 · INQ.31 · 1 mark · NAT

In the circuit given, the Thevenin equivalent resistance $R_{t h}$ across the terminals 'a' and 'b' is ________ $Ω$ (rounded off to one decimal place).

GATE 2023 IN question 31: Planar ladder circuit with a common bottom rail that is terminal b. — Figure from the GATE 2023 IN paper. It is part of the question.

Answer and solution

ANSWER

$R_{t h} = 1.0 Ω$

Official answer: 1.0Source: Official answer key, GATE 2023 IN (IIT Kanpur)

Deactivate the independent sources. The circuit has no dependent sources, so $R_{t h}$ is simply the resistance seen between a and b once the sources are switched off. Replace the $1 V$ source with a short circuit and each $1 A$ source with an open circuit.
Left end: the shorted $1 V$ source joins the top-left node to the bottom rail (terminal b). The left $1 Ω$ now sits across a short, so it carries no current and drops out. The top-left node is at the same potential as b.
Middle branch: the $1 A$ source is now an open, so its series $1 Ω$ carries no current and that branch drops out. The two top $1 Ω$ resistors are therefore in series, running from a to the top-left node, which is b: $1 + 1 = 2 Ω$ .
Right side: the branch with $1 Ω$ in series with the second $1 A$ source is also an open, so it drops out too. The last branch is the two $1 Ω$ resistors in series, straight from a to b: $1 + 1 = 2 Ω$ .
Combine the two paths in parallel across a-b: $R_{t h} = 2 Ω ∥ 2 Ω = \frac{2 \times 2}{2 + 2} = 1.0 Ω$

KEY IDEA

With only independent sources present, $R_{t h}$ is found by deactivating them: short every voltage source and open every current source. Any resistor in series with a current source then carries no current and drops out, and any resistor directly across a voltage source is shorted out.

WATCH OUT FOR

Keeping the $1 Ω$ resistors that sit in series with the $1 A$ sources in the network. Once a current source is opened, its whole branch carries no current, so those resistors do not count (keeping them gives about $0.46 Ω$ ). A second mistake is opening the $1 V$ source instead of shorting it. That leaves the left $1 Ω$ in the path and gives $3 ∥ 2 = 1.2 Ω$ .

From the GATE 2023 IN paper. Every question of this paper · Download the full paper · All 16 Theorems questions, with notes

GATE 2023 IN Q.31: solution and answer

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