Electrical Engineering Gate 2025 Questions with Answer

Ques 1 GATE 2025

Consider two coupled circuits, having self-inductances L₁ and L₂, that carry non-zero currents I₁ and I₂ respectively. The mutual inductance between the circuits is M with unity coupling coefficient. The stored magnetic energy of the coupled circuits is minimum at which of the following value(s) of I₁/I₂ ?

Ques 2 GATE 2025

The switch (S) closes at t=0 sec. The time, in sec, the capacitor takes to charge to 50 V is ______ (round off to one decimal place).

Ques 3 GATE 2025

A coil of inductance 100 mH and series resistance 100 Ω is connected across a 20 V, 1 kHz supply. The quality factor of the coil at 1 kHz is

Ques 4 GATE 2025

The current, i, in the circuit shown below, in A, is ______ (round off to the nearest integer).

Ques 5 GATE 2025

The I-V characteristics of the element between the nodes X and Y is best depicted by

A

B

C

D

Ques 6 GATE 2025

A nullator is defined as a circuit element where the voltage across the device and the current through the device are both zero. A series combination of a nullator and a resistor of value, R, will behave as a

Ques 7 GATE 2025

The maximum percentage error in the equivalent resistance of two parallel-connected resistors of 100 Ω and 900 Ω with each having a maximum 5% error is ______ % (round off to nearest integer value).

Ques 8 GATE 2025

Consider the state-space model ẋ(t)=Ax(t)+Br(t), y(t)=Cx(t) where x(t), r(t), y(t) are the state, input and output, respectively. The matrices A, B, C are given below

Ques 9 GATE 2025

A controller D(s) of the form (1+K_Ds) is to be designed for the plant G(s)=1000√2/(s(s+10)²) as shown in the figure.
The value of K_D that yields a phase margin of 45° at the gain cross-over frequency of 10 rad/sec is ______ (round off to one decimal place).

Ques 10 GATE 2025

The Nyquist plot of a strictly stable G(s) having the numerator polynomial as (s-3) encircles the critical point -1 once in the anti-clockwise direction. Which one of the following statements on the closed-loop system shown in figure, is correct?

Ques 11 GATE 2025

The open-loop transfer function of the system shown in the figure, is G(s)=Ks(s+2)/((s+5)(s+7)). For K≥0 which of the following real axis point(s) is/are on the root locus?

Ques 12 GATE 2025

A Boolean function is given as
f=(u̅+v̅+w̅+x̅).(u̅+v̅+w̅+x).(u̅+v+w̅+x̅).(u̅+v+w̅+x).
The simplified form of this function is represented by

A

B

C

D

Ques 13 GATE 2025

A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as cube of the speed. The motor is fed from a 400 V DC source and draws 40 A armature current. Assume linear magnetic circuit. The external resistance, in Ω, that must be connected in series with the armature to reduce the speed of the motor by half, is closest to