GATE 2004 Electrical Engineering
54 questions across 1 session
For a tachometer if $$\theta \left( t \right)$$ is the rotor displacement is radians, $$e\left( t \right)$$ is the output voltage and $${K_t}$$ is the tachometer constant in V/rad/...
Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$...
The armature resistance of a permanent magnet dc motor is 0.8 $$\Omega$$. At no load, the motor draws 1.5 A from a supply voltage of 25 V and runs at 1500 rpm. The efficiency of th...
A 8 pole, DC generator has a simplex wave-wound armature containing 32 coils of 6 turns each. Its flux per pole is 0.06 Wb. The machine is running at 250 rpm. The induced armature...
The resistance and reactance of a 100 kVA 11000|400 V, $$\triangle$$ - Y distribution transformer are 0.02 and 0.07 pu respectively. The phase impedance of the transformer referred...
A 500 kVA, 3-phase transformer has iron loses of 300 W and full load copper losses of 600 W. The percentage load at which the transformer is expected to have maximum efficiency is
The type of single-phase induction motor having the highest power factor at full load is
The direction of rotation of a 3-phase induction motor is clockwise when it is supplied with 3-phase sinusoidal voltage having phase sequence A-B-C. For counter clockwise rotation...
For a linear electromagnetic circuit, the following statement is true.
A rotating electrical machine having its self-inductances of both the stator and the rotor windings, independent of the rotor position will be definitely not develop
A single-phase, 230 V, 50 Hz, 4 pole, capacitor-start induction motor has the following stand still impedances Main winding Z m =6.0 + j4.0Ω Auxiliary winding Z a = 8.0 + j6.0Ω The...
A 400 V, 15 kW, 4 pole, 50 Hz, Y-connected induction motor has full load slip of 4%. The output torque of the machine at full load is
For a given stepper motor, the following torque has the highest numerical value.
The following motor definitely has a permanent magnet rotor
The $$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$...
The generalized circuit constants of a $$3$$-phase, $$220$$ $$kV$$ rated voltage, medium length transmission line are $$A = D = 0.936 + j\,0.016 = 0.936\angle {0.98^ \circ }$$ $$B...
For the equation, $${s^3} - 4{s^2} + s + 6 = 0$$ the number of roots in the left half of $$s$$ plane will be
A 500 MVA, 50 Hz, 3-phase turbo-generator produces power at 22 kV. Generator is Y-connected and its neutral is solidly grounded. Its sequence reactances are X 1 = X 2 = 0.15 and X...
A lightning stroke discharges impulse current of $$10$$ kA (peak) on a $$400$$ kV transmission line having surge impedance of $$250\,\Omega $$. The magnitude of transient over-volt...
Total instantaneous power supplied by a $$3$$-phase ac supply to a balanced $$R$$-$$L$$ load is
A $$400$$ $$V,$$ $$50$$ $$kVA,$$ $$0.8$$ $$pf$$ leading delta connected, $$50$$ $$Hz$$ synchronous machine has a synchronous reactance of $$2$$ $$ohm$$ and negligible armature resi...
Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$...
The transmission line distance protection relay having the property of being inherently directional is
The synchronous speed for the seventh space harmonic $$mmf$$ wave of a $$3$$-phase, $$8$$ pole, $$50$$ $$Hz$$ induction machine is
The unit impulse response of a second order under-damped system starting from rest is given by $$c\left( t \right) = 12.5{e^{ - 6t}}\,\sin 8t,\,\,t \ge 0.$$ The steady-state value...
A $$110$$ $$kV,$$ single core coaxial, XLPE insulated power cable delivering power at $$50$$ $$Hz,$$ has a capacitance of $$125$$ $$nF/km.$$ If the dielectric loss tangent of XLPE...
The open loop transfer function of a unity feedback control system is given as $$G\left( s \right) = {{as + 1} \over {{s^2}}}.$$. The value of $$‘a’$$ to give a phase margin of $${...
A $$500$$ $$MW$$ $$3$$-phase $$Y$$-connected synchronous generator has a rated voltage of $$21.5kV$$ at $$0.85$$ $$pf.$$ The line current when operating at full load rated conditio...
A $$800$$ $$kV$$ transmission line is having per phase line inductance of $$1.1$$ $$mH/km$$ and per phase line capacitance of $$11.68$$ $$nF/km.$$ Ignoring the length of the line,...
A unity feedback system, having an open loop gain becomes stable when $$G\left( s \right)H\left( s \right) = {{K\left( {1 - s} \right)} \over {\left( {1 + s} \right)}}$$
In thermal power plants, the pressure in the working fluid cycle is developed by
The rated voltage of a $$3$$-phase power system is given as
Two $$3$$-phase, $$Y$$-connected alternators are to be paralleled to a set of common bus bars. The armature has a per phase synchronous reactance of $$1.7\Omega $$ and negligible a...
A new generator having $${E_g} = 1.4\,\angle {30^ \circ }\,$$ pu [ equivalent to ($$1.212 +j$$ $$0.70$$)pu ] and synchronous reactance $$'{X_s}'$$ of $$1.0$$ pu on the system base,...
The state variable description of a linear autonomous system is, $$\mathop X\limits^ \bullet = AX,\,\,$$ where $$X$$ is the two dimensional state vector and $$A$$ is the system mat...
The inductance of a long solenoid of length $$1000$$ $$mm$$ wound uniformly with $$3000$$ turns on a cylindrical paper tube of $$60$$ $$mm$$ diameter is
A 50 Hz, 4-pole, 500 MVA, 22 kV turbo-generator is delivering rated megavolt-amperes at 0.8 power factor. Suddenly a fault occurs reducing is electric power output by 40%. Neglect...
A hydraulic turbine having rated speed of $$250$$ $$rpm$$ is connected to a synchronous generator. In order to produce power at $$50$$ $$Hz,$$ the number of poles required in the g...
Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$...
For harnessing low variable water heads, the suitable hydraulic turbine with high percentage of reaction and runner adjustable vanes is
A bipolar junction transistor $$(BJT)$$ is used as a power control switch by biasing it in the cut-off region (OFF state) or in the saturation region (ON state). In the ON state, f...
For a $$1.8$$ degree, $$2$$-phase bipolar stepper motor, the stepping rate is $$100$$ steps/second. The rotational speed of the motor in $$rpm$$ is
The simplified form of the Boolean expression $$Y = \left( {\overline A BC + D} \right)\left( {\overline A D + \overline B \overline C } \right)$$ can be written as
The area enclosed between the parabola $$y = {x^2}$$ and the straight line $$y=x$$ is _______.
A $$3$$-phase generator rated at $$110$$ MVA, $$11$$ kV is connected through circuit breakers to a transformer. The generator is having direct axis sub-transient reactance $$X'{'_d...
The Nyquist plot of loop transfer function $$G(s) H(s)$$ of a closed loop control system passes through the point $$(-1,j0)$$ in the $$G(s) H(s)$$ plane. The phase margin of the sy...
A bipolar junction transistor (BJT) is used as a power control switch by biasing it in the cutoff region (OFF state) or in the saturation region (ON state). In the ON state, for th...
The rms value of the resultant current in a wire which carries a dc current of 10 A and a sinusoidal alternating current of peak value 20 A is
A dc A-h meter is rated for 15 A, 250V. The meter constant is 14.4 A-sec/rev. The meter constant at rated voltage may be expressed as
A moving iron ammeter produces a full scale torque of $$240$$ $$\,\mu Nm$$ with a deflection of $${120^ \circ }$$ at a current of $$10$$ $$A$$. The rate of change of self inductanc...
The core flux in the $$CT$$ of above problem under the given operating condition is
A $$50$$ $$Hz,$$ bar primary $$CT$$ has a secondary with $$500$$ turns. The secondary supplies $$5A$$ current into a purely resistive burden of $$1\,\Omega $$. The magnetizing ampe...
A galvanometer with a full scale current of $$10$$ $$mA$$ has a resistance of $$1000$$$$\Omega $$. The multiplying power (the ratio of measured current to galvanometer current) of...
A moving coil of a meter has $$100$$ turns, and a length and depth of $$10$$ $$mm$$ and $$20$$ $$mm$$ respectively. It is positioned in a uniform radial flux density of $$200$$ $$m...