GATE 2026 EE Q.28: solution and answer

GATE 2026 · EEQ.28 · 1 mark · MCQ

Consider the circuit shown in Figure (a). A gate pulse $v_{g}$ is applied between time instants $t_{0}$ and $t_{1}$ . After $t_{1}$ , during the MOSFET turn OFF process, it experiences a voltage overshoot. Based on the $v_{d s}$ waveforms shown in Figure (b), which one of the following options is correct?

GATE 2026 EE question 28: Figure (a): a DC supply V_DC feeds, from its top rail, an inductor L in parallel with a series branch of a resistor R_f… — Figure from the GATE 2026 EE paper. It is part of the question.

(A)
$R_{1} > R_{2} > R_{3}$
(B)
$R_{1} > R_{3} > R_{2}$
(C)
$R_{3} > R_{2} > R_{1}$
(D)
$R_{2} > R_{3} > R_{1}$

Answer and solution

ANSWER

Option (B): $R_{1} > R_{3} > R_{2}$ .

Official answer: BSource: Official answer key, GATE 2026 EE (IIT Guwahati)

Between $t_{0}$ and $t_{1}$ the MOSFET is ON, so $v_{d s} \approx 0$ and the inductor current rises to a value $I_{L}$ at $t_{1}$ . With $v_{d s} \approx 0$ the diode in the $R_{f}$ branch is reverse biased, so that branch carries no current while the switch is ON.
At $t_{1}$ the MOSFET turns OFF. The inductor current cannot change instantly, so it is diverted into the loop drain node, $D$ , $R_{f}$ , the $V_{D C}$ rail and back through $L$ . The same current $I_{L}$ flows in $R_{f}$ at $t_{1}^{+}$ , whatever the value of $R_{f}$ .
Applying KVL around this loop gives the drain voltage just after turn-off: $v_{d s} (t_{1}^{+}) = V_{D C} + I_{L} R_{f} + V_{D},$ where $V_{D}$ is the small diode drop.
The overshoot above $V_{D C}$ is therefore $Δ v \approx I_{L} R_{f}$ . Since $I_{L}$ is the same for all curves, a larger $R_{f}$ gives a higher peak.
The decaying loop current has time constant $τ = L / R_{f}$ , so a larger $R_{f}$ also makes $v_{d s}$ settle to $V_{D C}$ faster. This agrees with the highest curve decaying fastest in Figure (b).
From Figure (b) the peak heights are highest for $R_{f} = R_{1}$ , then $R_{f} = R_{3}$ , then lowest for $R_{f} = R_{2}$ .
Since peak height rises with $R_{f}$ , $R_{1} > R_{3} > R_{2},$ which is option (B).

KEY IDEA

At turn-off the inductor current $I_{L}$ is forced through the freewheeling resistor $R_{f}$ , so the drain voltage jumps to $V_{D C} + I_{L} R_{f}$ . The overshoot is proportional to $R_{f}$ , and the peak ordering of the curves is the ordering of the resistances.

WATCH OUT FOR

Reading the lowest curve as the one with the largest resistance, or thinking a larger $R_{f}$ damps the spike. A larger $R_{f}$ gives a larger $I_{L} R_{f}$ jump, though it also makes the spike decay faster (smaller $L / R_{f}$ ).

From the GATE 2026 EE paper. Every question of this paper · Download the full paper · All 9 Switches questions, with notes

GATE 2026 EE Q.28: solution and answer

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