GATE Overflow for GATE IN - Questions without answers in Electrical Circuits and Machines

GATE IN 2026 | Question: 7

Mon, 23 Feb 2026 13:37:47 +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?

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

GATE IN 2026 | Question: 23

Mon, 23 Feb 2026 13:37:18 +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)

GATE IN 2026 | Question: 48

Mon, 23 Feb 2026 13:36:32 +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)

GATE IN 2025 | Question: 14

Thu, 06 Mar 2025 17:18:26 +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

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

GATE IN 2025 | Question: 15

Thu, 06 Mar 2025 17:18:24 +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 $33.69^{\circ}$

GATE IN 2025 | Question: 34

Thu, 06 Mar 2025 17:17:42 +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 $45\: \mathrm{kW}$

GATE IN 2025 | Question: 35

Thu, 06 Mar 2025 17:17:40 +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 $V_{\mathrm{C}}=4.5 \mathrm{~V}$

GATE IN 2025 | Question: 36

Thu, 06 Mar 2025 17:17:37 +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

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

GATE IN 2025 | Question: 50

Thu, 06 Mar 2025 17:17:12 +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).

GATE IN 2025 | Question: 51

Thu, 06 Mar 2025 17:17:11 +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).

GATE IN 2025 | Question: 53

Thu, 06 Mar 2025 17:17:08 +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).

GATE IN 2025 | Question: 55

Thu, 06 Mar 2025 17:17:05 +0000

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

GATE IN 2024 | Question: 20

Fri, 16 Feb 2024 18:41:00 +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).

GATE IN 2024 | Question: 23

Fri, 16 Feb 2024 18:41:00 +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).

GATE IN 2024 | Question: 41

Fri, 16 Feb 2024 18:40:56 +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).

GATE IN 2024 | Question: 51

Fri, 16 Feb 2024 18:40:53 +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).

GATE IN 2024 | Question: 52

Fri, 16 Feb 2024 18:40:53 +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).

GATE IN 2023 | Question: 2

Mon, 22 May 2023 00:15:02 +0000

Inductance of a coil is measured as $10 ~ \mathrm{mH}$, using an LCR meter, when no other objects are present near the coil. The LCR meter uses a sinusoidal excitation at $10 ~ \mathrm{kHz}$. If a pure copper sheet is brought near the coil, the same LCR meter will read ________.

less than $10 ~ \mathrm{mH}$
$10~ \mathrm{mH}$
more than $10 ~\mathrm{mH}$
less than $10~ \mathrm{mH}$ initially and then stabilizes to more than $10~ \mathrm{mH}$

GATE IN 2023 | Question: 20

Mon, 22 May 2023 00:14:41 +0000

When the bridge given below is balanced, the current through the resistor $\mathrm{R}_{\mathrm{a}}$ is____________ $\mathrm{mA}$ (rounded off to two decimal places).

GATE IN 2023 | Question: 21

Mon, 22 May 2023 00:14:40 +0000

In the circuit given, the Thevenin equivalent resistance $\mathrm{R}_{\mathrm{th}}$ across the terminals '$\mathrm{a}$' and ' $\mathrm{b}$' is____________$\Omega$ (rounded off to one decimal place).

GATE IN 2023 | Question: 24

Mon, 22 May 2023 00:14:37 +0000

The full-scale range of the wattmeter shown in the circuit is $100 \mathrm{~W}$. The turns ratio of the individual transformers are indicated in the figure. The RMS value of the ac source voltage $\mathrm{V}_{\mathrm{s}}$ is $200 \mathrm{~V}$. The wattmeter reading will be____________$\mathrm{W}$ (rounded off to the nearest integer).

GATE IN 2023 | Question: 25

Mon, 22 May 2023 00:14:36 +0000

The no-load steady-state output voltage of a $\text{DC}$ shunt generator is $200 \mathrm{~V}$ when it is driven in the clockwise direction at its rated speed. If the same machine is driven at the rated speed but in the opposite direction, the steady-state output voltage will be________________$\text{V}$ (rounded off to the nearest integer).

GATE IN 2023 | Question: 36

Mon, 22 May 2023 00:14:25 +0000

In the circuit shown, $\omega=100 \pi \mathrm{rad} / \mathrm{s}, \mathrm{R}_1=\mathrm{R}_2=2.2 \Omega$ and $\mathrm{L}=7 \mathrm{mH}$. The capacitance $C$ for which $Y_{\text {in }}$ is purely real is__________________$\mathrm{mF}$ (rounded off to two decimal places).

GATE IN 2023 | Question: 45

Mon, 22 May 2023 00:14:14 +0000

A sinusoidal current of $i_1(t)=1 \sin (200 \pi t) \mathrm{mA}$ is flowing through a $4~ \mathrm{H}$ inductor which is mutually coupled to another $5 ~ \mathrm{H}$ inductor carrying
$$
\mathrm{i}_2(t)=2 \sin (200 \pi t) \mathrm{~mA}
$$
as shown in the figure. The coupling coefficient between the inductors is $0.6.$ The peak energy stored in the circuit is_____________$\mu \mathrm{J}$ (rounded off to two decimal places).

GATE IN 2023 | Question: 48

Mon, 22 May 2023 00:14:10 +0000

A short-circuit test is conducted on a single-phase transformer by shorting its secondary. The frequency of input voltage is $1 ~ \mathrm{kHz}$. The corresponding wattmeter reading, primary current and primary voltage are $8 \mathrm{~W}, 2 \mathrm{~A}$ and $6 \mathrm{~V}$ respectively. Assume that the no-load losses and the no-load currents are negligible, and the core has linear magnetic characteristics. Keeping the secondary shorted, the primary is connected to a $2 \mathrm{~V}$ (RMS), $1 ~ \mathrm{kHz}$ sinusoidal source in series with a $\frac{1}{2 \pi \sqrt{5}} ~\mathrm{mF}$ capacitor. The primary current (RMS) will be_______________$\text{A}$ (rounded off to two decimal places).

GATE IN 2023 | Question: 50

Mon, 22 May 2023 00:14:08 +0000

In the circuit shown, the input voltage $\mathrm{V}_{\text {in }}=100 ~ \mathrm{mV}$. The switch and the opamp are ideal. At time $\mathrm{t}=0$, the initial charge stored in the $10 ~ \mathrm{nF}$ capacitor is $1 ~ \mathrm{nC}$, with the polarity as indicated in the figure. The switch $\mathrm{S}$ is controlled using a $1 ~ \mathrm{kHz}$ squarewave voltage signal $\mathrm{V}_{\mathrm{s}}$ as shown. Whenever $\mathrm{V}_{\mathrm{s}}$ is 'High', $\mathrm{S}$ is in position '$1$' and when $\text{V}_\text{s}$ is 'Low', $\text{S}$ is in position '$2$'.

At $t=20 \mathrm{~ms}$, the magnitude of the voltage $\mathrm{V}_{\mathrm{o}}$ will be______________$\mathrm{mV}$ (rounded off to the nearest integer).

GATE IN 2023 | Question: 55

Mon, 22 May 2023 00:13:48 +0000

The voltage source $\mathrm{Vs}=10 \sqrt{2} \sin (20000 \pi t) ~ \mathrm{V}$ has an internal resistance of $50~ \Omega$. The RMS value of the current through $\mathrm{R}$ is_________$\text{mA}$ (rounded off to one decimal place).

*This option did not appear in $\text{GATE 2023}$ Examination. It appeared as "Turbine flow meter", that is, "Turbine flow meter" option was repeated.

GATE IN 2022 | Question: 19

Sun, 20 Mar 2022 17:33:58 +0000

A $\text{440 V, 8 kW, 4-pole, 50 Hz,}$ star-connected induction motor has a full load slip of $0.04.$ The rotor speed (in rpm) at full load is ________ (round off to one decimal place)

GATE IN 2022 | Question: 42

Sun, 20 Mar 2022 17:33:56 +0000

In the circuit shown, the load is driven by a sinusoidal ac voltage source $V_{1} =100 \; \angle 0^{\circ} \; \text{V}$ at $50 \; \text{Hz}.$ Given $R_{1}=20 \; \Omega, C_{1} = \left(\frac{1000}{\pi}\right) \mu \text{F, L}_{1} = \left(\frac{20}{\pi}\right) \; \text{mH} $ and $R_{2} = 4 \; \Omega,$ the power factor is _________ (round off to one decimal place)

GATE IN 2022 | Question: 44

Sun, 20 Mar 2022 17:33:56 +0000

Given Circuit $\text{A}$ with currents $I_{1}$ and $I_{2}$ as shown, the current $I_{3}$ in Circuit $\text{B}$ (in amperes), is _________ (round off to one decimal place)

GATE IN 2022 | Question: 45

Sun, 20 Mar 2022 17:33:56 +0000

In the balanced three-phase circuit shown, $C_{0} = 8.2 \; \mu \text{F}$ and the line-to-line $\text{r.m.s.}$ voltage is $440 \; \text{V}$ at $50 \; \text{Hz}.$ The reading on the wattmeter (in watts) is ________ (round off to two decimal places)

GATE IN 2022 | Question: 47

Sun, 20 Mar 2022 17:33:56 +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)

GATE IN 2022 | Question: 52

Sun, 20 Mar 2022 17:33:55 +0000

In the circuit shown, the capacitance $C_{0}=10 \; \mu \text{F}$ and inductance $\text{L}_{0} = 1 \; \text{mH}$ and the diode is ideal. The capacitor is initially charged to $10 \; \text{V}$ and the current in the inductor is initially zero. If the switch is closed at $t=0 \; \text{s},$ the voltage $V_{c}(t)$ (in volts) across the capacitor at $t=0.5 \; \text{s}$ is (round off to one decimal place)

GATE IN 2021 | Question: 27

Fri, 19 Feb 2021 15:48:37 +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

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

GATE IN 2021 | Question: 28

Fri, 19 Feb 2021 15:48:37 +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

GATE IN 2021 | Question: 42

Fri, 19 Feb 2021 15:48:36 +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).

GATE IN 2021 | Question: 49

Fri, 19 Feb 2021 15:48:35 +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) ____________.

GATE IN 2021 | Question: 52

Fri, 19 Feb 2021 15:48:34 +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 ________.

GATE2020 IN: 25

Tue, 03 Nov 2020 14:26:44 +0000

Two $100\: \Omega$ resistors having tolerance $3\%$ and $4\%$ are connected in series. The effective tolerance of the series combination $\text{(in % rounded off to one decimal place)}$ is ___________.

GATE2020 IN: 30

Tue, 03 Nov 2020 14:26:43 +0000

$I_1,\; I_2\: and \:I_3$ in the figure below are mesh currents. The correct set of mesh equations for these currents, in matrix form, is ____________

$\begin{bmatrix} 3&-1&-2\\-1&3&-1\\-2&-1&3 \end{bmatrix} \begin{bmatrix}I_1\\I_2\\I_3\end{bmatrix}= \begin{bmatrix}V_1\\V_2\\-V_3\end{bmatrix}$
$\begin{bmatrix} 3&-1&-2\\-1&3&-1\\-2&-1&-3 \end{bmatrix} \begin{bmatrix}I_1\\I_2\\I_3\end{bmatrix}= \begin{bmatrix}V_1\\V_2\\V_3\end{bmatrix}$
$\begin{bmatrix} -3&-1&-2\\-1&3&-1\\-2&-1&3 \end{bmatrix} \begin{bmatrix}I_1\\I_2\\I_3\end{bmatrix}= \begin{bmatrix}V_1\\V_2\\-V_3\end{bmatrix}$
$\begin{bmatrix} 1&-1&-2\\-1&2&-1\\-2&-1&3 \end{bmatrix} \begin{bmatrix}I_1\\I_2\\I_3\end{bmatrix}= \begin{bmatrix}V_1\\V_2\\V_3\end{bmatrix}$

GATE2020 IN: 33

Tue, 03 Nov 2020 14:26:43 +0000

The rms value of the phasor current $\underline{I}$ in the circuit shown $\text{(in amperes)}$ is _____.

GATE2020 IN: 34

Tue, 03 Nov 2020 14:26:43 +0000

In the circuit shown, the rms value of the voltage across the $ 100 \Omega$ resistor $\text{(in volts)}$ is _________.

GATE2020 IN: 42

Tue, 03 Nov 2020 12:52:22 +0000

The real power drawn by a balanced load connected to a $\text{400 V, 50 Hz,}$ balanced, symmetrical 3-phase, 3-wire, $RYB$ sequence mains is measured using the two-wattmeter method. Wattmeter $W_1$ is connected in the $R$ line and wattmeter $W_2$ is connected in the $B$ line. The line current is measured as $\frac{1}{\sqrt3}A$. If the wattmeter $W_1$ reads zero, the reading on $W_2$ (in watts) is _______.

GATE2020 IN: 54

Tue, 03 Nov 2020 12:52:20 +0000

In the Maxwell-Wien bridge shown, the detector D reads zero when $C_1=100 nF$ and $R_1=100 k\Omega$. The Q factor of the coil is ______

GATE2020: 4

Tue, 03 Nov 2020 04:24:37 +0000

In the circuit shown below, the safe maximum value for the current $I$ is _______

$\text{1.0 A}$
$\text{0.5 A}$
$\text{0.1 A}$
$\text{0.05 A}$

GATE2020: 18

Tue, 03 Nov 2020 04:24:36 +0000

Three $400\;\Omega$ resistors are connected in delta and powered by a $400\;V\;(rms), \;50\;Hz,$ balanced symmetrical $R-Y-B$ sequence, three-phase three-wire mains. The rms value of the line current $\text{(in amperes, rounded off to one decimal place)}$ is __________.

GATE IN 2017 | Question: 31

Mon, 02 Nov 2020 00:06:48 +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 _________.

GATE IN 2017 | Question: 32

Mon, 02 Nov 2020 00:06:48 +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 _________.

GATE IN 2017 | Question: 48

Mon, 02 Nov 2020 00:05:07 +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 ____________.

GATE IN 2017 | Question: 29

Mon, 02 Nov 2020 00:00:20 +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 __________$H$.