GATE 2026 EC Q.17: solution and answer

GATE 2026 · ECQ.17 · 1 mark · MCQ

The ideal OP-AMP circuit shown in the Figure produces output voltage $V_{o} = x$ when the Switch, S, is open.

Which of the options represents the output voltage when S is closed?

GATE 2026 EC question 17: Non-inverting amplifier using an ideal op-amp. — Figure from the GATE 2026 EC paper. It is part of the question.

(A)
$x$
(B)
$\frac{2}{3} x$
(C)
$\frac{3}{4} x$
(D)
$\frac{1}{2} x$

Answer and solution

ANSWER

When S is closed the output voltage is $\frac{3}{4} x$ (it falls from 4 V to 3 V). The answer is (C).

Official answer: CSource: Official answer key, GATE 2026 EC (IIT Guwahati)

Assume an ideal op-amp: the virtual short gives $V_{-} = V_{+} = V_{i} = 1 V$ , and no current flows into either input. The circuit is a non-inverting amplifier with $R_{1} = 1 k Ω$ from the inverting node to ground and a feedback resistance $R_{f}$ from the inverting node to the output.
KCL at the inverting node: the current through $R_{1}$ is $\frac{V _{-}}{R _{1}}$ and all of it flows through $R_{f}$ , so $\frac{V _{o} - V _{-}}{R _{f}} = \frac{V _{-}}{R _{1}}$ . This gives the non-inverting gain $\frac{V _{o}}{V _{i}} = 1 + \frac{R _{f}}{R _{1}} .$
S open: the feedback path is the $2 k Ω$ resistor in series with the $1 k Ω$ resistor, so $R_{f} = 3 k Ω$ and $x = V_{o} = (1 + \frac{3 k Ω}{1 k Ω}) (1 V) = 4 V .$
S closed: S is wired from the junction of the two feedback resistors straight to the output, which puts it across the output-side $1 k Ω$ resistor. Closing it shorts that resistor, leaving $R_{f} = 2 k Ω$ .
Output with S closed: $V_{o}^{'} = (1 + \frac{2 k Ω}{1 k Ω}) (1 V) = 3 V .$
Ratio: $\frac{V _{o}^{'}}{x} = \frac{3 V}{4 V} = \frac{3}{4}$ , so $V_{o}^{'} = \frac{3}{4} x$ . This is option (C).

KEY IDEA

For an ideal non-inverting amplifier, $V_{o} = (1 + \frac{R _{f}}{R _{1}}) V_{i}$ . Closing S shorts the $1 k Ω$ feedback resistor, so $R_{f}$ drops from $3 k Ω$ to $2 k Ω$ and the gain drops from 4 to 3. The ratio of the two outputs is the ratio of the two gains, $3/4$ .

WATCH OUT FOR

Taking the ratio of the feedback resistances ( $R_{f}^{'} / R_{f} = 2/3$ , option B) instead of the ratio of the gains. A non-inverting gain is $1 + R_{f} / R_{1}$ , not $R_{f} / R_{1}$ , so the '1 +' term has to be kept. Another slip is using the inverting-amplifier formula $- R_{f} / R_{1}$ , which also gives $2/3$ for the ratio.

From the GATE 2026 EC paper. Every question of this paper · Download the full paper · All 36 Op-amps questions, with notes

GATE 2026 EC Q.17: solution and answer

Answer and solution

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