# GATE Questions & Answers of Electric Circuits Electrical Engineering

#### Electric Circuits 120 Question(s) | Weightage 16 (Marks)

The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is

In the figure, the voltages are $v_1(t)=100\cos\left(wt\right),\;v_2(t)=100\cos\left(wt+\mathrm\pi18\right)\;\;$ and $v_3(t)=100\cos\left(wt+\mathrm\pi36\right)$. The circuit is in sinusoidal steady state, and $R<<wL.P_1,P_2\;$ and $P_3$ are the average power outputs. Which one of the following statements is true?

In the two-port network shown, the $\style{font-family:'Times New Roman'}{h_{11}}$ parameter $\style{font-family:'Times New Roman'}{\left(where\;h_{11}=\frac{V_1}{I_1}\;when\;V_2=0\right)}$ in ohms is _____________ (up to 2 decimal places).

A DC voltage source is connected to a series L-C circuit by turning on the switch S at time $t=0$ as shown in the figure. Assume $i(0)=0,v(0)=0$ . Which one of the following circular loci represents the plot of $i(t)$ versus $v(t)\;?$

The equivalent impedance $Z_{eq}$ for the infinite ladder circuit shown in the figure is

A three-phase load is connected to a three-phase balanced supply as shown in the figure. If $V_{an}=100\angle0^\circ\;$ V ,$V_{bn}=100\angle-120^\circ\;$ V and $V_{cn}=100\angle-240^\circ\;$ V  (angles are considered positive in the anti-clockwise direction), the value of R for zero current in the neutral wire is ___________$\Omega$ (up to 2 decimal places).

The voltage across the circuit in the figure, and the current through it, are given by the following expressions

$v(t)=5-10\;\cos\left(wt+60^\circ\right) V$

$i(t)=5+X\;\cos\left(wt\right)A$

where $w=100\mathrm\pi$ radian/s. If the average power delivered to the circuit is zero, then the value of $\mathrm X$ (in Ampere) is _____ (up to 2 decimal places).

The voltage $v(t)$ across the terminals a and b as shown in the figure, is a sinusoidal voltage having a frequency $w=100$radian/s. When the inductor current $i(t)$ is in phase with the voltage $v(t)$, the magnitude of the impedance Z (in $\mathrm\Omega$) seen between the terminals a and b is ________ (up to 2 decimal places).

A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $V_{an}=220\;\sin\left(100\;\mathrm{πt}\right)\;V$ and $i_a=10\;\sin\left(100\;\mathrm{πt}\right)\;A,$ respectively. Similarly for phase-b, the instantaneous voltage and current are $V_{bn}=220\;\cos\left(100\;\mathrm{πt}\right)\;V$ and $i_b=10\;\cos\left(100\;\mathrm{πt}\right)\;A,$, respectively.

The total instantaneous power flowing from the source to the load is

The power supplied by the 25 V source in the figure shown below is _________ W.

The equivalent resistance between the terminal A and B is__________$\Omega$.

Two passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port 1.

Given

$\begin{array}{l}V_1=A_1V_2+B_1I_2\\I_1=C_1V_2+D_1I_2\\V_2=A_2V_3+B_2I_3\\I_2=C_2V_3+D_2I_3\end{array}$

$A1,\;B1,\;C1,\;D1,\;A2,\;B2,\;C2$ and $D_2$ are the generalized circuit constants. If the Thevenin equivalent circuit at port 3 consists of a voltage source $V_T$ and an impendence $Z_T$ , connected in series, then

The switch in the figure below was closed for a long time. It is opened at t = 0. The current in the inductor of 2 H for , is

In the circuit shown below, the maximum power transferred to the resistor R is ______________ W.

The figure shows the power per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where $\alpha$ is a complex number with non-zero real and imaginary parts.

For the given circuit, Ybus and Zbus are bus admittance matrix and bus impedance matrix, respectively, each of size 2 × 2. Which one of the following statements is true?

For the given 2-port network, the value of transfer impedance z21 in ohms is__________

The initial charge in the 1 F capacitor present in the circuit shown is zero. The energy in joules transferred from the DC source until steady state condition is reached equals_________.(Give the answer up to one decimal place.)

For the balanced Y-Y connected 3-phase in the figure below, the line-line voltage is 208 V rms and the total power absorbed by the load is 432 W at a power factor of 0.6 leading.

The approximate value of the impedance Z is

In the circuit shown below, the value of capacitor C required for maximum power to be transferred to the load is

For the network given in figure below, the Thevenin’s voltage Vab is

RA and RB are the input resistances of circuits as shown below. The circuits extend infinitely in the direction shown. Which one of the following statements is TRUE?

In the portion of a circuit shown, if the heat generated in 5 Ω resistance is 10 calories per second, then heat generated by the 4 Ω resistance, in calories per second, is _______.

In the given circuit, the current supplied by the battery, in ampere, is _______.

If an ideal transformer has an inductive load element at port 2 as shown in the figure below, the equivalent inductance at port 1 is

In the circuit shown, switch S2 has been closed for a long time. At time $t=0$ switch S1 is closed. At $t=0^+$, the rate of change of current through the inductor, in amperes per second, is _____.

In the circuit shown below, the supply voltage is $10\mathrm{sin}\left(1000t\right)$ volts. The peak value of the steady state current through the 1 Ω resistor, in amperes,

A dc voltage with ripple is given by $v\left(t\right)=\left[100+10\mathrm{sin}\left(\omega t\right)-5\mathrm{sin}\left(3\omega t\right)\right]$ volts. Measurements of this voltage $v\left(t\right)$, made by moving-coil and moving-iron voltmeters, show readings of V1 and V2 respectively. The value of V2V1, in volts, is _________.

The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the admittance of the circuit becomes a pure conductance at all frequencies is _____________.

In the circuit shown below, the node voltage VA is ___________ V.

The following figure shows the connection of an ideal transformer with primary to secondary turns ratio of 1:100. The applied primary voltage is 100 V (rms), 50 Hz, AC. The rms value of the current I, in ampere, is __________.

A resistance and a coil are connected in series and supplied from a single phase, 100 V, 50 Hz ac source as shown in the figure below. The rms values of plausible voltages across the resistance (VR) and coil (VC) respectively, in volts, are

The voltage (V) and current (A) across a load are as follows.

$v\left(t\right)=100\mathrm{sin}\left(\omega t\right)$ ,

The average power consumed by the load, in W, is___________.

In the circuit shown below, the voltage and current sources are ideal. The voltage (Vout) across the current source, in volts, is

The graph associated with an electrical network has 7 branches and 5 nodes. The number of independent KCL equations and the number of independent KVL equations, respectively, are

The driving point input impedance seen from the source Vs of the circuit shown below, in Ω, is ______.

The $z$-parameters of the two port network shown in the figure are . The average power delivered to ${R}_{L}=20\Omega$ , in watts, is _______.

In the balanced 3-phase, 50 Hz, circuit shown below, the value of inductance (L) is 10 mH. The value of the capacitance (C) for which all the line currents are zero, in millifarads, is ___________.

In the circuit shown below, the initial capacitor voltage is 4 V. Switch $S_1$ is closed at $t=0$. The charge (in $\mu C$) lost by the capacitor from $t=25\;\mu$s to $t=100\;\mu$s is ____________.

The voltages developed across the 3 Ω and 2 Ω resistors shown in the figure are 6V and 2V respectively, with the polarity as marked. What is the power (in Watt) delivered by the 5V voltage source?

For the given circuit the Thevenin equivalent is to be determined. The Thevenin voltage,${V}_{Th}$(in volt), seen from terminal AB is _________.

An inductor is connected in parallel with a capacitor as shown in the figure.

As the frequency of current i is increased, the impedance (Z) of the network varies as

The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in volt) is given by v(t) = 12 sin t. If the circuit is in steady-state, then the rms value of the current (in Ampere) flowing in the circuit is ______.

In a linear two-port network, when 10 V is applied to Port 1, a current of 4 A flows through Port 2 when it is short-circuited. When 5 V is applied to Port 1, a current of 1.25 A flows through a 1 $\mathrm{\Omega }$ resistance connected across Port 2. When 3 V is applied to Port 1, then current (in Ampere) through a 2 $\mathrm{\Omega }$ resistance connected across Port 2 is _________.

In the given circuit, the parameter k is positive, and the power dissipated in the 2 $\mathrm{\Omega }$ resistor is 12.5W. The value of k is________.

A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero initial conditions, the value of $\frac{{\mathrm{d}}^{2}i}{\mathrm{d}{t}^{2}}$ at t = ${0}^{+}$ is

The current i (in Ampere) in the 2 $\mathrm{\Omega }$ resistor of the given network is ____ .

In the given network V, ${V}_{2}=100\angle -{120}^{°}$V, ${V}_{3}=100\angle +{120}^{°}$V. The phasor current i (in Ampere) is

A symmetrical square wave of 50% duty cycle has amplitude of ±15 V and time period of 0.4π ms. This square wave is applied across a series RLC circuit with R = 5$\mathrm{\Omega }$, L = 10 mH, and C = 4μF. The amplitude of the 5000 rad/s component of the capacitor voltage (in Volt) is __________.

Two identical coils each having inductance L are placed together on the same core. If an overall inductance of $\alpha$L is obtained by interconnecting these two coils, the minimum value of $\alpha$ is ________.

The three circuit elements shown in the figure are part of an electric circuit. The total power absorbed by the three circuit elements in watts is __________.

C0 is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If, half of the entire gap as shown in figure (b) is filled with a dielectric of permittivity ${\mathit{\in }}_{r}$, the expression for the modified capacitance is

A combination of 1 µF capacitor with an initial voltage${\nu }_{c}\left(0\right)=-2\nu$ in series with a 100 O resistor is connected to a 20 mA ideal dc current source by operating both switches at t = 0 s as shown. Which of the following graphs shown in the options approximates the voltage vs across the current source over the next few seconds?

An incandescent lamp is marked 40 W, 240V. If resistance at room temperature (26°C) is 120 Ω, and temperature coefficient of resistance is 4.5x10-3/°C, then its ‘ON’ state filament temperature in °C is approximately _______

In the figure, the value of resistor R is (25 + I/2) ohms, where I is the current in amperes. The current I is ______

The following four vector fields are given in Cartesian co-ordinate system. The vector field which does not satisfy the property of magnetic flux density is

Two identical coupled inductors are connected in series. The measured inductances for the two possible series connections are 380 μH and 240 μH. Their mutual inductance in μH is ________

The switch SW shown in the circuit is kept at position ‘1’ for a long duration. At t = 0+, the switch is moved to position ‘2’. Assuming |Vo2| > |Vo1|, the voltage vc(t) across the capacitor is

A parallel plate capacitor consisting two dielectric materials is shown in the figure. The middle dielectric slab is placed symmetrically with respect to the plates.

If the potential difference between one of the plates and the nearest surface of dielectric interface is 2 Volts, then the ratio ε1 : ε2 is

Assuming an ideal transformer, the Thevenin’s equivalent voltage and impedance as seen from the terminals x and y for the circuit in figure are

The voltage across the capacitor, as shown in the figure, is expressed as

${V}_{c}\left(t\right)={A}_{1}\mathrm{sin}\left({\omega }_{1}t-{\theta }_{1}\right)+{A}_{2}\mathrm{sin}\left({\omega }_{2}t-{\theta }_{2}\right)$

The values of  A 1and  A 2 respectively, are

The total power dissipated in the circuit, shown in the figure, is 1 kW.

The voltmeter, across the load, reads 200 V. The value of  XL is ___________.

The magnitude of magnetic flux density $\left(\overrightarrow B\right)$ at a point having normal distanced meters from an infinitely extended wire carrying current of I A is$\frac{{\mu }_{0}I}{2\pi d}$ (in SI units). An infinitely extended wire is laid along the x-axis and is carrying current of 4 A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction. ${\mu }_{0}$ is permeability of free space. Assume $\widehat i$, $\widehat j$, $\widehat k$ to be unit vectors along x, y and z axes respectively

Assuming right handed coordinate system, magnetic field intensity, $\overrightarrow H$ at coordinate (2,1,0) will be

The line A to neutral voltage is A1015oV for a balanced three phase star-connected load with phase sequence ABC. The voltage of line B with respect to line C is given by

The driving point impedance Z(s) for the circuit shown below is

A non-ideal voltage source Vs has an internal impedance of Zs. If a purely resistive load is to be chosen that maximizes the power transferred to the load, its value must be

The Norton’s equivalent source in amperes as seen into the terminals X and Y is _______.

The power delivered by the current source, in the figure, is ________.

A series RLC circuit is observed at two frequencies. At ω1=1 krad/s, we note that source voltage ${V}_{1}=100\angle {0}^{o}V$ results in a current ${I}_{1}=0.03\angle {31}^{o}A$. At ${\omega }_{2}=2$ krad/s, the source voltage ${V}_{2}=100\angle {0}^{o}V$ results in a current ${I}_{1}=2\angle {31}^{o}A$. The closest values for R,L,C out of the following options are

A source ${\nu }_{s}\left(t\right)=V\mathrm{cos}100\pi t$ has an internal impedance of $\left(4+j3\right)\mathrm{\Omega }$.If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in $\mathrm{\Omega }$ should be

The flux density at a point in space is given by $\mathbf{B}\mathbf{=}4x{\mathbf{a}}_{\mathrm{x}}+2ky{\mathbf{a}}_{\mathbf{y}}+8{\mathbf{a}}_{\mathbf{z}}$ Wb/m2. The value of constant k must be equal to

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding star equivalent will be scaled by a factor of

In the circuit shown below, if the source voltage ${V}_{s}=100\angle 53.13°\mathrm{V}$ then Thevenin’s equivalent voltage in Volts as seen by the load resistance RL is

Three capacitors C1, C2, and C3, whose values are 10μF, 5μF, and 2μF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown, the maximum safe voltage in Volts that can be applied across the combination and the corresponding total charge in μC stored in the effective capacitance across the terminals are respectively

Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective resistances are R1 and R2. When connected in series, their effective Q factor at the same operating frequency is

The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage VWX1 = 100V is applied across WX to get an open circuit voltage VYZ1  across YZ. Next, an ac voltage VYZ2  = 100V is applied across YZ to get an open circuit voltage VWX2  across WX. Then, VYZ1/VWX1,VWX2/VYZ2 are respectively,

In the circuit shown below, the current through the inductor is

The impedance looking into nodes 1 and 2 in the given circuit is

A two-phase load draws the following phase currents: ${i}_{1}\left(t\right)={I}_{m}\mathrm{sin}\left(\omega t-{\Phi }_{1}\right)$, ${i}_{2}\left(t\right)={I}_{m}\mathrm{cos}\left(\omega t-{\Phi }_{2}\right)$.These currents are balanced if ${\Phi }_{1}$ is equal to

The average power delivered to an impedance (4-j3)$\Omega$ by a current $5\mathrm{cos}\left(100\pi t+100\right)A$ is

In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is

If VA-VB=6V, then VC-VD is

(i) 1Ω connected at port B draws a current of 3 A
(ii) 2.5Ω connected at port B draws a current of 2 A