GATE Electrical Engineering

Consider two coupled circuits having self inductances $L_1$ and $L_2$ that carry non-zero currents $I_1$ and $I_2$ respectively. The mutual inductance between the circuit is $M$ wi...

Using shunt capacitors, the power factor of a 3-phase, 4 kV induction motor (drawing 390 kVA at 0.77 pf lag) is to be improved to 0.85 pf lag. The line current of the capacitor ban...

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 o...

The input voltage $v(t)$ and current $i(t)$ of a converter are given by, $v(t)=300 \sin (\omega t) \mathrm{V}$ $$ i(t)=10 \sin \left(\omega t-\frac{\pi}{6}\right)+2 \sin \left(3 \o...

For a two-phase network, the phase voltages $V_p$ and $V_q$ are to be expressed in terms of sequence voltages $V_\alpha$ and $V_\beta$ as $\begin{bmatrix} V_p \\ V_q \end{bmatrix}...

The transfer function of a real system, H(s), is given as: $$H(s) = {{As + B} \over {{s^2} + Cs + D}}$$, where A, B, C and D are positive constants. This system cannot operate as

An inductor having a Q-factor of 60 is connected in series with a capacitor having a Q-factor of 240. The overall Q-factor of the circuit is ________. (round off to nearest integer...

Two single-core power cables have total conductor resistances of $0.7 \Omega$ and $0.5 \Omega$ respectively and their insulation resistances (between core and sheath) are $600 \mat...

A signal generator having a source resistance of $50 \Omega$ is set to generate a 1 kHz sinewave. Open circuit terminal voltage is 10 V peak-to-peak. Connecting a capacitor across...

A benchtop dc power supply acts as an ideal 4 A current source as long as its terminal voltage is below 10 V. Beyond this point, it begins to behave as an ideal 10 V voltage source...

A resistor and a capacitor are connected in series to a 10 V dc supply through a switch. The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ,...

A 0.1 μF capacitor charged to 100 V is discharged through a 1 kΩ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to...

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 minim...

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 5V is applied to Port1, a current of 1.25 A flo...

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 line A to neutral voltage is $$10\angle15^\circ\;V$$ for a balanced three phase star-connected load with phase sequence ABC. The voltage of line B with respect to line C is giv...

An incandescent lamp is marked 40W, 240V. If resistance at room temperature $$\left(26^\circ\mathrm C\right)\;\mathrm{is}\;120\mathrm\Omega$$ and temperature coefficient of resista...

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

A series RLC circuit is observed at two frequencies. At $$\omega_1$$ = 1k rad / s, we note that source voltage $$V_1=100\angle0^\circ V$$ results in a current $$I_1=0.03\angle31^\c...

A source $$v_s\left(t\right)=V\cos100\mathrm{πt}$$ has an internal impedance of (4 + j3) Ω.If a purely resistive load connected to this source has to extract the maximum power out...

Two magnetically uncoupled inductive coils have Q factors q 1 and q 2 at the chosen operating frequency. Their respective resistances are R 1 and R 2 . When connected in series, th...

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

A two phase load draws the following phase currents: $$i_1\left(t\right)=I_m\sin\left(\omega t-\phi_1\right)$$, $$i_2\left(t\right)=I_m\cos\left(\omega t-\phi_2\right)$$. These cur...

The voltage applied to a circuit is $$100\sqrt2\cos\left(100\mathrm{πt}\right)$$ volts and the circuit draws a current of $$10\sqrt2\;\sin\left(100\mathrm{πt}+\mathrm\pi/4\right)$$...

How many 200 W/200 V incandescent lamps connected in series would consume the same total power as a single 100 W/200 V incandescent lamp?

The Thevenin's equivalent of a circuit operating at $$\omega = 5\,\,rad/s\,\,{V_{oc}} = 3.71\angle - {15.9^ \circ }$$ and $${Z_0} = 2.38 - j0.667\Omega .$$ At this frequency, the m...

A three phase balanced star connected voltage source with frequency $$\omega \,\,rad/s$$ is connected to a star connected balanced load which is purely inductive. The instantaneous...

A $$3$$ $$V$$ $$dc$$ supply with an internal resistance of $$2$$ $$\Omega $$ supplies a passive non-linear resistance characterized by the relation $${V_{NL}} = {{\rm I}^2}{}_{NL}$...

The matrix $$A$$ given below is the node incidence matrix of a network. The columns correspond to braches of the network while the rows correspond to nodes. Let $$V = {\left[ {{v_1...

A $$400V$$, $$50$$ $$Hz,$$ three phase balanced source supplies power to a star connected load whose rating is $$12\,\,\angle 3\,\,kVA,$$ $$0.8$$ $$pf$$ (lag). The rating $$($$in $...

An ideal capacitor is charged to a voltage $${V_0}$$ and connected at $$t=0$$ across an ideal inductor $$L.$$ (The circuit now consists of a capacitor and inductor alone). If we le...

A coil of inductance $$10$$ $$H$$ resistance $$40\,\,\Omega $$ is connected as shown in Fig. After the switch $$S$$ has been in connection with point $$1$$ for a very long time, it...

The $$Z$$ matrix of a $$2$$ $$-$$ port network is given by $$\left[ {\matrix{ {0.9} & {0.2} \cr {0.2} & {0.6} \cr } } \right].$$ The element $${Y_{22}}$$ vof the corresponding $$Y$...

A balanced delta connected load of $$\left( {8 + j6} \right)$$ $$\Omega $$ per phase is connected to a $$400V,$$ $$50Hz,$$ $$3-$$ phase supply lines. If the input power factor is t...

The graph of an electrical network has $$N$$ nodes and $$B$$ branches. The number of links, $$L$$, with respect to the choice of a tree, is given by

A series $$R-L-C$$ circuit has $$R = 50\Omega ;$$ $$L=100$$ $$\mu H$$ and $$C = 1\,\,\mu F.$$ The lower half power frequency of the circuit is

A first order, low pass filter is given with $$R = 50\,\,\Omega $$ and $$C$$ $$ = 5\mu F.$$ What is the frequency at which the gain of the voltage transfer function of the filter i...

Given two coupled inductors $${L_1}$$ and $${L_2}$$, their mutual inductance $$M$$ satisfies

In a series $$RLC$$ circuit at resonance, the magnitude of the voltage developed across the capacitor

Two incandescent light bulbs of $$40$$ $$W$$ and $$60$$ $$W$$ rating are connected in series across the mains. Then

A passive 2-port network is in a steady state.Compare to its input, the steady state output can never offer

A unit step voltage is applied at $$t = 0$$ to a series $$RL$$ circuit with zero initial conditions.

A two-port device is defined by the following pair of equations: $${i_1} = 2{v_1} + {v_2}$$ and $${i_2} = {v_1} + {v_2}$$ Its impedance parameters $$\left( {{z_{11}},\,\,{z_{12}},\...

A voltage wafeform $$v\left( t \right) = 12\,{t^2}$$ is applied across a $$1$$ $$H$$ inductor for $$t \ge 0,$$ with initial current through it being zero. The current through the i...

If an $$ac$$ voltage wave is corrupted with an arbitrary number of harmonics, then the overall voltage waveform differs from its fundamental frequency component in terms of

A fixed capacitor of reactance –$$j0.02$$ $$\Omega $$ is connected in parallel across a series combination of a fixed inductor of reactance $$j0.01$$ $$\Omega $$ and a variable res...

Currents $${{\rm I}_1},\,{{\rm I}_2}$$ and $${{\rm I}_3}$$ meet at a junction (node) in a circuit. All currents are marked as entering the node. If $${{\rm I}_1} = - 6\sin \left( {...

When a periodic triangular voltage peak amplitude $$1$$ $$V$$ and frequency $$0.5$$ $$Hz$$ is applied to a parallel combination of $$1\,\Omega $$ resistance and $$1$$ $$F$$ capacit...

The voltage phasor of a circuit is $$10\angle {15^0}\,V$$ and the current phasor is $$2\,\,\angle - {45^0}A.$$ The active and the reactive powers in the circuit are

A series $$R-L-C$$ circuit when excited by a $$10$$ $$V$$ sinusoidal voltage source of variable frequency, exhibits resonance at $$100$$ $$Hz$$ and has a $$3$$ $$dB$$ bandwidth of...

The $$RMS$$ value of half $$-$$ wave rectified symmetrical square wave current of $$2A$$ is

When a resistor $$R$$ is connected to a current source, it consumes a power of $$18$$ $$W.$$ when the same $$R$$ is connected to a voltage source having the same magnitude as the c...

A rectangular voltage pulse of magnitude $$V$$ and duration $$T$$ is applied to a series combination of resistance $$R$$ and capacitance $$C.$$ The maximum voltage developed across...

A circuit with a resistor, inductor and capacitor in series is resonant at $${f_0}\,\,Hz.$$ If all the component values are now doubled, the new resonant frequency is

A sinusoidal source of voltage $$V$$ and frequency $$f$$ is connected to a series circuit of variables resistance, $$R$$ and a fixed reactance, $$X.$$ The locus of the tip of the c...

A circuit consisting of a single resistor $$R$$ and an inductor $$L$$ in series is driven by a $$25$$ $$V$$ $$rms,$$ $$50$$ $$Hz$$ sinusoidal voltage source. A capacitor is to be p...

A $$10$$ $$V$$ battery with an internal resistance of $$1\,\Omega $$ is connected across a nonlinear load whose $$V-1$$ characteristic is given by $$7{\rm I} = {V^2} + 2V.$$ The cu...

Energy stored in a capacitor over a cycle, when excited by an $$a.c.$$ source is

Two identical coils of negligible resistance when connected in series across a $$200V,$$ $$50$$ $$Hz$$ source draws, a current of $$10$$ $$A.$$ When the terminals of one of the coi...

A coil (which can be modeled as a series $$RL$$ circuit) has been designed for high $$-$$ $$Q$$ performance at a rated voltage and a specified frequency. If the frequency of operat...

A series $$R-L-C$$ circuit has the following parameter values: $$R = 10\Omega ,\,\,L = 0.01\,H,\,\,C = 100\,\,m\,\,F.$$ The $$Q$$ factor of the circuit at resonance is

If a two-port network is passive, then we have, with the usual notation, the following relationship

Superposition principle is not applicable to a network containing time-varying registors.