GATE Overflow for GATE IN - Recent activity in Electrical Circuits and Machines

Edited: GATE IN 2026 | Question: 48

Thu, 26 Mar 2026 07:44:41 +0000

A single phase transformer has a rating of $10 \mathrm{kVA}, 50 \mathrm{~Hz}, 1100 \mathrm{~V} / 220 \mathrm{~V}$. In an open circuit test with the high voltage side open, the following are obtained:

Voltage applied to the low voltage winding $=220 \mathrm{~V}$
Measured power $=363 \mathrm{~W}$
Measured current $=2.75 \mathrm{~A}$

Magnetizing reactance $X_{m}$ referred to the high voltage winding is $\_\_\_\_$ $\Omega$. (rounded off to the nearest integer)

Edited: GATE IN 2026 | Question: 23

Sat, 21 Mar 2026 08:08:25 +0000

In a series $R L$ circuit shown in the figure, the current through the resistor lags the AC source voltage by $45^{\circ}$. Let $R=100 \pi \Omega$ and $L=2 \mathrm{H}$.

The frequency of the source is $\_\_\_\_\_\_$ $\mathrm{Hz}$. (rounded off to the nearest integer)

Edited: GATE IN 2026 | Question: 7

Sat, 21 Mar 2026 07:32:16 +0000

A single phase step-down transformer has a high voltage primary winding and a low voltage secondary winding. The secondary winding is connected to a load impedance $Z_{2}$. The impedance $Z_{2}$ when referred to the primary winding is denoted by $Z_{2}^{\prime}$. Which of the following conditions is true?

$Z_{2}^{\prime}=Z_{2}$
$0.5 Z_{2} < Z_{2}^{\prime} < Z_{2}$
$Z_{2}^{\prime}>Z_{2}$
$Z_{2}^{\prime} \leq 0.5 Z_{2}$

Edited: GATE IN 2024 | Question: 52

Sat, 29 Nov 2025 18:32:18 +0000

A three-phase squirrel-cage induction motor has a starting torque of $100 \%$ of the full load torque and a maximum torque of $300 \%$ of the full load torque. Neglecting the stator impedance, the slip at the maximum torque is $\_\_\_\_\_\_\%$ (rounded off to two decimal places).

Edited: GATE IN 2024 | Question: 51

Sat, 29 Nov 2025 18:31:54 +0000

A $50 \mathrm{~kVA}$ transformer has an efficiency of $95 \%$ at full load and unity power factor. Assume the core losses are negligible. The efficiency of the transformer at $75 \%$ of the full load and $0.8$ power factor is $\_\_\_\_\_\_\%$ (rounded off to one decimal place).

Edited: GATE IN 2024 | Question: 41

Sat, 29 Nov 2025 13:21:53 +0000

In the figure shown, $\mathrm{R}=4.5 \mathrm{~k} \Omega, \Delta \mathrm{R}=1.5 \mathrm{~k} \Omega$, and $\mathrm{INA}$ is assumed to be ideal. The equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is$\_\_\_\_\_\_ \mathrm{~k} \Omega$ (rounded off to nearest integer).

Edited: GATE IN 2024 | Question: 23

Sat, 29 Nov 2025 13:06:12 +0000

The switch in the following figure has been closed for a long time $(t<0)$. It is opened at $t=0$ seconds. The value of $d v_{0} / d t$ at $t=0^{+}$is $\_\_\_\_\_\_ ~ \mathrm{V} / \mathrm{s}$ (rounded off to nearest integer).

Edited: GATE IN 2024 | Question: 20

Sat, 29 Nov 2025 13:00:32 +0000

The voltage applied and the current drawn by a circuit are

$$ \begin{array}{c} v(t)=95+200 \cos (120 \pi t)+90 \cos \left(360 \pi t-60^{\circ}\right) \mathrm{V} \\
i(t)=4 \cos \left(120 \pi t-60^{\circ}\right)+1.5 \cos \left(240 \pi t-75^{\circ}\right) \mathrm{A}
\end{array} $$

The average power absorbed by the circuit is $\_\_\_\_\_\_ \mathrm{~W}$ (rounded off to nearest integer).

Edited: GATE IN 2025 | Question: 55

Mon, 19 May 2025 10:08:40 +0000

For the circuit shown in the figure, the active power supplied by the source is ___________ $W$ (rounded off to one decimal place).

Edited: GATE IN 2025 | Question: 53

Mon, 19 May 2025 10:06:15 +0000

In the circuit shown, the switch is opened at $t=0 \mathrm{~s}$. The current $i(t)$ at $t=2 \mathrm{~ms}$ is __________ $\mathrm{mA}$ (rounded off to two decimal places).

Edited: GATE IN 2025 | Question: 51

Mon, 19 May 2025 10:02:38 +0000

In the circuit shown, the galvanometer $(G)$ has an internal resistance of $100 \: \Omega$. The galvanometer current $I_{G}$ is ____________ $\mu \mathrm{A}$ (rounded off to the nearest integer).

Edited: GATE IN 2025 | Question: 50

Mon, 19 May 2025 10:01:38 +0000

The circuit given in the figure is driven by a voltage source $V_{S}=25 \sqrt{2} \angle 30^{\circ} \: \mathrm{V}$. The system is operating at a frequency of $50 \: \mathrm{Hz}$ . The transformers are assumed to be ideal. The average power dissipated, in $W$, in the $50 \: \mathrm{k} \Omega$ resistance is ____________ (rounded off to two decimal places).

Edited: GATE IN 2025 | Question: 36

Mon, 19 May 2025 08:27:42 +0000

A $2$-pole, $50 \mathrm{~Hz}, 3$-phase induction motor supplies power to a certain load at $2970 \: \mathrm{rpm}$ . The torque-speed curve of this machine follows a linear relationship between synchronous speed and $95 \%$ of synchronous speed. Assume mechanical and stray losses to be zero. If the load torque of the motor is doubled, the new operating speed of the motor, in $\mathrm{rpm}$, is

$2940$
$2812$
$2970$
$2850$

Edited: GATE IN 2025 | Question: 35

Mon, 19 May 2025 08:24:08 +0000

The bridge circuit, shown in Figure (a), can be equivalently represented using the circuit shown in Figure (b). The values of $R_{1}, R_{2}$, and $V_{\mathrm{C}}$ in the equivalent circuit are

$R_{1}=6 \: \mathrm{k} \Omega, R_{2}=3 \mathrm{k} \Omega$, and $V_{\mathrm{C}}=9 \mathrm{~V}$
$R_{1}=3 \: \mathrm{k} \Omega, R_{2}=6 \mathrm{k} \Omega$, and $V_{\mathrm{C}}=4.5 \mathrm{~V}$
$R_{1}=2 \:\mathrm{k} \Omega, R_{2}=2 \mathrm{k} \Omega$, and $V_{\mathrm{C}}=9 \mathrm{~V}$
$R_{1}=2 \: \mathrm{k} \Omega, R_{2}=2 \mathrm{k} \Omega$, and $V_{\mathrm{C}}=4.5 \mathrm{~V}$

Edited: GATE IN 2025 | Question: 34

Mon, 19 May 2025 08:10:12 +0000

Power consumed by a three-phase balanced load is measured using two-wattmeter method. The per-phase average power drawn by the load is $30 \: \mathrm{kW}$ at $\frac{\sqrt{3}}{2}$ lagging power factor. The readings of the wattmeters will be

$15 \: \mathrm{kW}$ and $15\: \mathrm{kW}$
$22.5\: \mathrm{kW}$ and $7.5\: \mathrm{kW}$
$60\: \mathrm{kW}$ and $30\: \mathrm{kW}$
$45\: \mathrm{kW}$ and $45\: \mathrm{kW}$

Edited: GATE IN 2025 | Question: 15

Mon, 19 May 2025 07:22:19 +0000

Three parallel admittances $Y_{a}=-j 0.2 \mathrm{~S}, Y_{b}=0.3 \mathrm{~S}$, and $\quad Y_{c}=j 0.4 \mathrm{~S}$ connected in parallel with a voltage source $V_{s}=10 \angle 45^{\circ} \: \mathrm{V}$, draw a total current $I_{s}$ from the source. The currents flowing through each of these admittances are $I_{a}, I_{b}$, and $I_{c}$, respectively. Let $I=I_{b}+I_{c}$. The phase relation between $I$ and $I_{s}$ is

$I$ leads $I_{s}$ by $19.44^{\circ}$
$I$ lags $I_{s}$ by $19.44^{\circ}$
$I$ leads $I_{s}$ by $33.69^{\circ}$
$I$ lags $I_{s}$ by $33.69^{\circ}$

Edited: GATE IN 2025 | Question: 14

Mon, 19 May 2025 07:20:37 +0000

The circuit shown in Figure (a) can be represented using its equivalent T-model as shown in Figure (b). The values of the inductances $L_{1}, L_{2}$, and $L_{3}$ in the equivalent T-model are

$L_{1}=7 \mathrm{H}, L_{2}=6 \mathrm{H}, L_{3}=-4 \mathrm{H}$
$L_{1}=-1 \mathrm{H}, L_{2}=-2 \mathrm{H}, L_{3}=4 \mathrm{H}$
$L_{1}=3 \mathrm{H}, L_{2}=2 \mathrm{H}, L_{3}=9 \mathrm{H}$
$L_{1}=1 \mathrm{H}, L_{2}=-2 \mathrm{H}, L_{3}=-4 \mathrm{H}$

Recategorized: GATE IN 2022 | Question: 47

Mon, 21 Apr 2025 15:25:46 +0000

A conducting semi-circular loop of radius $R=0.1 \; \text{m}, $ with its diameter centered at the origin, rotates in the $x-y$ plane about the origin with a constant angular velocity, $\omega= 20 \; \text{rad/s},$ as shown. A magnetic field of magnitude $B=2T$ and normal to $x-y$ plane exists in the region $x \ge 0$ as shown. If the loop has a resistance of $2 \; \Omega,$ and negligible inductance, the peak-to-peak current (in milliamperes) in the loop is ___________ (round off to one decimal place)

Recategorized: GATE IN 2021 | Question: 28

Mon, 21 Apr 2025 15:24:39 +0000

A slip-ring induction motor is expected to be started by adding extra resistance in the rotor circuit. The benefit that is derived by adding extra resistance in the rotor circuit in comparison to the rotor being shorted is

The starting torque would be higher
The power factor at start will be lower
The starting current is higher
The losses at starting would be lower

Recategorized: GATE IN 2021 | Question: 27

Mon, 21 Apr 2025 15:24:36 +0000

A single-phase transformer has maximum efficiency of $98 \%$. The core losses are $\text{80 W}$ and the equivalent winding resistance as seen from the primary side is $0.5 \:\Omega$. The rated current on the primary side is $\text{25 A}$. The percentage of the rated input current at which the maximum efficiency occurs is

$35.7\%$
$50.6\%$
$80.5\%$
$100\%$

Recategorized: GATE IN 2021 | Question: 42

Mon, 21 Apr 2025 15:24:13 +0000

A household fan consumes $\text{60 W}$ and draws a current of $\text{0.3125 A (rms)}$ when connected to a $\text{230 V (rms) ac }$, $\text{50 Hz}$ single phase mains. The reactive power drawn by the fan in $\text{VAr}$ is _______________________ (rounded off to the nearest integer).

Recategorized: GATE IN 2021 | Question: 52

Mon, 21 Apr 2025 15:24:02 +0000

In the bridge circuit shown, the voltmeter $\text{V}$ showed zero when the value of the resistors are: $R_{1}=100\:\Omega$, $R_{2}=110\:\Omega$, and $R_{3}=90\:\Omega$. If $\left ( R_{1}/R_{2} \right )=\left ( R_{A}/R_{B} \right )$, the value of $R_{4}$ is ohm is ________.

Recategorized: GATE IN 2021 | Question: 49

Mon, 21 Apr 2025 15:23:59 +0000

The power in a $\text{400 V}$ ($\text{rms}$, line-line) three-phase, three-wire $\text{RYB}$ sequence system is measured using the two wattmetters, as shown. The $\text{R}$-line current is $5\angle 60^\circ \:A$. Wattmeter $W_{1}$ in the $\text{R}$-line will read (in watt) ____________.

Recategorized: GATE2019 IN: 4

Mon, 21 Apr 2025 15:23:14 +0000

In the Figures (a) and (b) shown below, the transformers are identical and ideal ,except that the transformer in Figure (b) is centre -tapped. Asssuming ideal diodes, the ratio of the root mean-square (RMS) voltage across the resistor R in Figure (a) to that in figure (b) is

$\sqrt{2}$: 1
2: 1
2$\sqrt{2}$ : 1
4:1

Recategorized: GATE2019 IN: 19

Mon, 21 Apr 2025 15:23:06 +0000

In the circuit shown below, initially the switch S${_1}$ is open, then capacitor C1 has a charge of 6 coulomb, and the capacitor C2 has 0 coulomb. After s${_1}$ is closed, the charge on C2 in steady state is $\_\_\_\_\_$ coulomb.

Recategorized: GATE2019 IN: 18

Mon, 21 Apr 2025 15:23:03 +0000

Consider a circuit comprising only resistors with constant resistance and ideal independent DC voltage sources. If all the resistances are scaled down by a factor 10, and all source voltages are scaled up by a factor 10, the power dissipated in the circuit scles up by a factor of $\_\_\_\_\_\_$.

Recategorized: GATE2019 IN: 17

Mon, 21 Apr 2025 15:23:00 +0000

In the circuit shown below, maximum power is transferred to the load resistance R${_L}$, when R${_L}$ = $\_\_\_\_$ $\Omega$.

Recategorized: GATE2019 IN: 44

Mon, 21 Apr 2025 15:22:18 +0000

In the circuit shown below, a step input voltage of magnitude 5 V is applied at node A at time t = 0. If the capacitor has no charge for t $\leq$ 0, the voltage at node P at t=6 ${\mu}$s is $\_\_\_\_$ V.(Answer should be rounded off to two decimal places)

Recategorized: GATE2019 IN: 45

Mon, 21 Apr 2025 15:22:00 +0000

In the circuit shown below, the angular frequency $\omega$ at which the current is in phase with the voltage is $\_\_\_\_\_\_$ rad/s.

Recategorized: GATE2018IN: 31

Mon, 21 Apr 2025 15:20:44 +0000

In the figure, an RLC load supplied by a 230 V, 50 Hz single phase source. The magnitude of the reactive power (in VAr) supplied by the source is $\_\_\_\_\_$.

Recategorized: GATE2018IN:30

Mon, 21 Apr 2025 15:20:42 +0000

In the given circuit, superposition is applied.When V$_2$ is set to 0 V, the current I$_2$ is -6 A. When V$_1$ is set to 0 v, the current I$_1$ is + 6A. Current I$_3$ (in A) when both sources are applied will be (up to two decimal places)$\_\_\_\_\_$.

Recategorized: GATE2018IN: 32

Mon, 21 Apr 2025 15:20:32 +0000

In the given circuit, the mesh currents $I{_1}$,$I{_2}$ and $I{_3}$ are

$I{_1}$ = 1 A, $I{_2}$ =2 A and $I{_3}$ = 3A
$I{_1}$ = 2 A, $I{_2}$ = 3 A and $I{_3}$ = 4A
$I{_1}$ = 3 A, $I{_2}$ = 4 A and $I{_3}$ = 5A
$I{_1}$ = 4 A, $I{_2}$ = 5 A and $I{_3}$ = 6A

Recategorized: GATE2018IN: 8

Mon, 21 Apr 2025 15:19:55 +0000

A coil having an impedance of (10 + j100) $\Omega$ is connected in parallel to a variable capacitor as shown in figure. Keeping the excitation frequency unchanged, the value of the capacitor is changed so that parallel resonance occurs. The impedance across terminals p-q at resonance (in $\Omega$) is $\_\_\_\_$.

Recategorized: GATE2018IN: 6

Mon, 21 Apr 2025 15:19:52 +0000

A series R-C circuit is excited by a 1 <0 V sinusoidal ac voltage source. The locus diagram of the phasor current L = (x + jy)A, when C is varied, while keeping R fixed, is

Recategorized: GATE2018IN: 7

Mon, 21 Apr 2025 15:19:41 +0000

The Thevenin equivalent circuit representation across terminals p – q of the circuit shown in the figure is a

1 V source in series with 150k$\Omega$
1 V source in parallel with 100k$\Omega$
2 V source in series with 150k$\Omega$
2 V source in parallel with 200k$\Omega$

Recategorized: GATE IN 2017 | Question: 32

Mon, 21 Apr 2025 15:19:27 +0000

In the circuit diagram, shown in the figure, $S_1$ was closed and $S_2$ was open for a very long time. At $t=0,\;S_1$ is opened and $S_2$ is closed. The voltage across the capacitor, in volt, at $t=5\mu s$ is _________.

Recategorized: GATE IN 2017 | Question: 31

Mon, 21 Apr 2025 15:19:24 +0000

A series $R-L-C$ circuit is excited with an a.c. voltage source. The quality factor $(Q)$ of the circuit is given as $Q=30$. The amplitude of current in $\text{ampere}$ at upper half-power frequency will be _________.

Recategorized: GATE IN 2017 | Question: 48

Mon, 21 Apr 2025 15:19:02 +0000

In the a.c. bridge, shown in the figure, $R=10^3$ $\Omega$ and $C=10^{-7}$ $F$. If the bridge is balanced at a frequency $\omega_\circ$, the value of $\omega_\circ$ in $\text{rad/s}$ is ____________.

Recategorized: GATE IN 2017 | Question: 29

Mon, 21 Apr 2025 15:18:12 +0000

The current response of a series $\text R-L$ circuit to a unit step voltage is given in the table. The value of $L$ is __________$H$.

Recategorized: GATE IN 2017 | Question: 30

Mon, 21 Apr 2025 15:18:09 +0000

For the circuit, shown in the figure, the total real power delivered by the source to the loads is _____________$\text{kW}$.

Recategorized: GATE IN 2017 | Question: 8

Mon, 21 Apr 2025 15:18:03 +0000

A circuit consisting of dependent and independent sources is shown in the figure. If the voltage at $\text{Node-1}$ is $-1\;\text{V}$, then the voltage at $\text{Node-2}$ is _____________ $\text{V}$.

Recategorized: GATE IN 2017 | Question: 6

Mon, 21 Apr 2025 15:17:58 +0000

A series $\text {R-L-C}$ circuit is excited with a $50\;\text{V}$, $50\;\text{Hz}$ sinusoidal source. The voltages across the resistance and the capacitance are shown in the figure. The voltage across the inductor $\text(V_L)$ is ___________$\text{V}$.

Recategorized: GATE2016-10

Mon, 21 Apr 2025 15:17:19 +0000

In the circuit shown below $ (v_1+v_2) =[1\; \sin(2\pi10000t)] + 1\;\sin(2\pi30000t)] \;V.$ The $RMS$ value of the current through the resistor $R$ will be minimum if the value of the capacitor $C$ in $\text{microfarad}$ is ____________.

Recategorized: GATE2016-6

Mon, 21 Apr 2025 15:17:07 +0000

Three currents $i_1, i_2$ and $i_3$ meet at a node as shown in the figure below. If $i_1=3\cos(\omega t)$ ampere, $i_2=4\sin(\omega t)$ ampere and $i_3=I_3\cos(\omega t+\theta)$ ampere, the value of $I_3$ in $\text{ampere}$ is $\_\_\_\_\_\_\_.$

Recategorized: GATE2016-35

Mon, 21 Apr 2025 15:16:14 +0000

The voltage $v(t)$ shown below is applied to the given circuit. $v(t)=3V$ for $t<0$ and $v(t)=6V$ for $t>0$. The value of current $i(t)$ at $t=1s$, in ampere is ____________.

Recategorized: GATE2016-33

Mon, 21 Apr 2025 15:16:11 +0000

A symmetrical three-phase three-wire $RYB$ system is connected to a balanced delta-connected load. The $RMS$ values of the line current and line-to-line voltage are $\text{10 A}$ and $\text{400 V}$ respectively. The power in the system is measured using the two wattmeter method. The first wattmeter connected between $R$-line and $Y$-line reads zero. The reading of the second wattmeter (connected between $B$-line and $Y$-line) in $\text{watt}$ is ___________.

Recategorized: GATE2016-32

Mon, 21 Apr 2025 15:16:05 +0000

In the circuit shown below, $V_s=101\angle 0V, R=10\Omega$ and $\omega L=100\Omega$. The current $I_s$ is in phase with $V_s$. The magnitude of $I_s$ in $\text{milliampere}$ is $\_\_\_\_\_\_\_\_.$

Recategorized: GATE2016-31

Mon, 21 Apr 2025 15:16:02 +0000

The current $I_X$ in the circuit given below in $\text{milliampere}$ is $\_\_\_\_\_\_\_.$

Recategorized: GATE2015-20

Mon, 21 Apr 2025 15:15:07 +0000

The output voltage of the ideal transformer with the polarities and dots shown in the figure is given by

$NV_i\sin \omega t$
$-NV_i\sin \omega t$
$\frac{1}{N}V_i\sin \omega t$
$-\frac{1}{N}V_i\sin \omega t$

Recategorized: GATE2015-16

Mon, 21 Apr 2025 15:15:04 +0000

The capacitor shown in the figure is initially charged to $\text{+10 V}$. The switch closes at time $t=0$. Then the value of $V_C(t)$ in volts at time $\text{t=0 ms}$ is _____________ $V$.