GATE 2001 Electrical Engineering
42 questions across 1 session
The electric field $$\overrightarrow E $$ (in volts/metre) at the point $$(1, 1, 0)$$ due to a point charge of $$+1$$ $$\mu C$$ located at $$\left( { - 1,\,1,\,1} \right)$$ (coordi...
An op-amp has an open-loop gain of $${10^5}$$ and an open-loop upper cutoff frequency of $$10$$ $$Hz.$$ If this op-amp is connected as an amplifier with a closed-loop gain of $$100...
A synchronous generator is connected to an infinite bus through a lossless double circuit transmission line. The generator is delivering 1.0 per unit power at a load angle of $${30...
A passive 2-port network is in a steady state.Compare to its input, the steady state output can never offer
In case of an armature controlled separately excited dc motor drive with closed loop speed control, an inner current loop is useful because it
An electric motor with 'constant output power' will have a torque speed characteristic in the form of a
A single-phase transformer is to be switched to the supply to have minimum inrush current. The switch should be closed at
The core flux of a practical transformer with a resistive load
A 3-phase transformer has rating of 20 MVA, 220 kV (star) / 33 kV (delta) with leakage reactance of 12%. The transformer reactance (in ohms) referred to each phase of the L.V. delt...
The hysteresis loop of a magnetic material has an area of 5 cm 2 with the scales given as 1 cm = 2 AT and 1 cm = 50 mWb. At 50 Hz, the total hysteresis loss is
It is desirable to eliminate 5 th harmonic voltage from the phase voltage of an alternator. The coils should be short-pitched by an electrical angle of
X d , X d ' and X d " are steady stated-axis synchronous reactance, transient d-axis reactance and sub-transient d-axis reactance of a synchronous machine respectively. Which of th...
Given the homogeneous state-space equation $$\mathop X\limits^ \bullet = \left[ {\matrix{ { - 3} & 1 \cr 0 & { - 2} \cr } } \right]x$$ the steady state value of $$\,\,{x_{ss}}\,\,...
A unit step voltage is applied at $$t = 0$$ to a series $$RL$$ circuit with zero initial conditions.
The conductors of a $$10$$ $$km$$ long, single phase, two wire line are separated by a distance of $$1.5$$ $$m.$$ The diameter of each conductor is $$1$$ $$cm.$$ If the conductors...
A 132 kV transmission line AB is connected to a cable BC. The characteristic impedances of the overhead line and the cable are 400$$\Omega $$ and 80$$\Omega $$ respectively. Assume...
Given the potential function in free space to be $$V\left( x \right) = \left( {50{x^2} + 50{y^2} + 50{z^2}} \right)$$ volts, the magnitude (in volts /metre) and the direction of th...
An Intel $$8085$$ processor is executing the program given below. $$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,MVIA,\,\,10H \cr & \,\,\,\,\,\,\,\,\,\...
Two incandescent light bulbs of $$40$$ $$W$$ and $$60$$ $$W$$ rating are connected in series across the mains. Then
Among the following four, the slowest $$ADC$$ (analog-to-digital converter) is
Given the characteristic equation $${s^3} + 2{s^2} + Ks + K = 0.$$ Sketch the root focus as $$K$$ varies from zero to infinity. Find the angle and real axis intercept of the asympt...
A lossless radial transmission line with surge impedance loading
A sample-and-hold $$(S/H)$$ circuit, having a holding capacitor of $$0.1$$ $$nF,$$ is used at the input of an $$ADC$$ (analog-to-digital converter). The conversion time of the $$AD...
In a series $$RLC$$ circuit at resonance, the magnitude of the voltage developed across the capacitor
Given two coupled inductors $${L_1}$$ and $${L_2}$$, their mutual inductance $$M$$ satisfies
The output of a logic gate is $$''1''$$ when all its inputs are at logic $$''0''.$$ The gate is either
A $$75$$ MVA, $$10$$ kV synchronous generator has X d $$= 0.4$$ p.u. The X d value (in p.u.) is a base of $$100$$ MVA, $$11$$ kV is
An $$N$$-channel $$JFET$$ having a pinch-off voltage $$\left( {{V_P}} \right)$$ of $$-5V$$ shows a transconductance (gm) of $$1$$ $$mA/V$$ when the applied Gate to source voltage $...
A power system has two synchronous generators. The Governor-turbine characteristics corresponding to the generators are P 1 = 50(50 – f), P 2 = 100 (51 – f) Where f denotes the sys...
A power system has two generators with the following cost curves Generator $$1:$$ $${C_1}\left( {{P_{G1}}} \right) = 0.006\,P_{G1}^2 + 8{P_{G1}} + 350$$ (Thousand Rupees/Hour) Gene...
A unity feedback system has an open-loop transfer function of $$G\left( s \right) = {{10000} \over {s{{\left( {s + 10} \right)}^2}}}$$ (a) Determine the magnitude of $$G\left( {j\o...
Two identical synchronous generators, each of $$100$$ $$MVA,$$ are working in parallel supplying $$100$$ $$MVA$$ at $$0.8$$ lagging $$p.f.$$ at rated voltage. Initially the machine...
For the $$Y$$-$$bus$$ matrix given in per unit values, where the first, second, third and fourth row refers to bus $$1, 2, 3$$ and $$4$$ respectively, draw the reactance diagram. $...
A $$50$$ $$kW$$ synchronous motor is tested by driving it by another motor. When the excitation is not switched on, the driving motor takes $$800$$ $$W.$$ When the armature is shor...
A $$50$$ Hz alternator is rated $$500$$ $$MVA,$$ $$20$$ $$kV,$$ with $${X_d} = 1.0$$ per unit and $$X'{'_d} = 0.2$$ per unit. It supplies a purely resistive load of $$400$$ $$MW$$...
A single line-to-ground fault occurs on an unloaded generator in phase a positive, negative, and zero sequence impedances of the generator are j0.25 p.u., j0.25 p.u., and j0.15 p.u...
An op-amp, having a slew rate of $$62.8$$ $$V/\mu \,$$sec, is connected in a voltage follower configuration. If the maximum amplitude of the input sinusoidal is $$10$$ Volts. Then...
The conductors of a $$10$$ km long, single phase, two wire line are separated by a distance of $$1.5$$ m. The diameter of each conductor is $$1$$ cm. If the conductors are of coppe...
A $$100$$ $$\mu A$$ ammeter has an internal resistance of $$100\,\Omega $$. For extending its range to measure $$500$$ $$\mu A$$, the shunt required is of resistance (in $$\Omega $...
Resistances $${R_1}$$ and $${R_2}$$ have, respectively, nominal values of $$10\Omega $$ and $$5\Omega ,$$ and tolerances of $$ \pm 5\% $$ and $$ \pm 10\% $$. The range of values fo...
The minimum number of wattmeter(s) required to measure 3 $$-$$ phase, 3 $$-$$ wire balanced or unbalanced power is
Given the relationship between the input $$u(t)$$ and the output $$y(t)$$ to be $$y\left( t \right) = \int\limits_0^t {\left( {2 + t - \tau } \right){e^{ - 3\left( {t - \tau } \rig...