GATE 1999 Electrical Engineering
51 questions across 1 session
Find the eigen values and eigen vectors of the matrix $$\left[ {\matrix{ 3 & { - 1} \cr { - 1} & 3 \cr } } \right]$$
The mobility of an electron in a conductor expressed in terms of
As temperature is increased, the voltage across a diode carrying a constant current.
The colour code of a $$1k\Omega $$ resistance is
An industrial consumer has a daily load pattern of $$2000$$ $$kW$$, $$0.8$$ lag for $$12$$ Hrs. and $$1000$$ $$kW$$ $$UPF$$ for $$12$$ Hrs. The load factor is
A separately excited $$DC$$ shunt motor is driving a fan load whose torque is proportional to the square of the speed. When $$100$$ $$V$$ are applied to the motor, the current take...
Corona losses are minimized when
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 $${{\rm I}_1} = - 6\sin \left( {...
$$A$$ $$220$$ kV, $$20$$ km long, $$3$$-phase transmission line has the following $$A, B, C, D$$ constants. $$A=D=0.96$$$$\angle {3^0},$$ $$\,B = 55\angle {65^0}\,\,\Omega /$$ phas...
An electromagnetic field is radiated from
A 4-pole lap-wound DC generator has a developed power of P watts and voltage of E volts. Two adjacent brushes of the machine are removed as they are worn out. If the machine operat...
A DC shunt motor is running at 1200 rmp, when excited with 220 V DC. Neglecting the losses and saturation, the speed of the motor when connected to a 175 V DC supply is:
A 10 kVA, 400 V/200 V, single phase transformer with a percentage resistance of 3% and percentage reactance of 6% is supplying a current of 50 A to a resistive load. The value of t...
A 400V/100V, 10 kVA two-winding transformer is reconnected as an autotransformer across a suitable voltage source. The maximum rating of such an arrangement could be
The percentage resistance and percentage reactance of a 10 kVA, 400 V/200 V, 3-phase transformer are 2% and 10% respectively. If the constant losses in the machine are 1%, the maxi...
The windings of a Q kVA, $$\frac{V_1}{V_2}$$ Volt, three-phase, Delta connected, core type transformer are reconnected to work as a single phase transformer. The maximum voltage an...
Starting torque can be obtained in the case of a single phase induction motor with identical main and auxiliary windings by connecting
The following starting method for an induction motor is inferior view of the poor starting torque per ampere of the line current drawn:
Higher synchronous reactance is preferred in the present day alternators, because one can have
A three phase alternator is wound with a 60 degree phase-spread armature windings and develops 300 kVA. If the armature is reconnected utilizing all the coils for single phase oper...
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...
A charge $$+Q$$ is uniformly distributed throughout the volume of a dielectric sphere of radius $$R$$ and dielectric constant $$'{\varepsilon _R}'.$$ Based on Gauss law, determine...
The logic function $$f = \overline {\left( {x.\overline y } \right) + \left( {\overline x .y} \right)} $$ is the same as
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 66 kV, 3-phase, 50 Hz, 150 km long overhead transmission line is open circuited at the receiving end. Each conductor has a resistance of 0.25$$\Omega $$/km, an inductive reactanc...
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...
Determine the magnitudes of the symmetrical components ($${{{\rm I}_{R1}},\,{{\rm I}_{R2}}\,}$$ and $${{{\rm I}_{R0}}}$$) of the currents in a three phase (RYB) three wire system,...
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 load carrying capability of a long AC transmission line is
Two parallel wires separated by a distance $$'d'$$ are carrying a current $$'{\rm I}'$$ in the same direction. The magnetic field along a line running parallel to these wires at mi...
A $$PWM$$ switching scheme is used with a three phase inverter to
A 3-phase, 11 kV, 50 Hz, 200 kW load has a power factor of 0.8 lag. A delta connected 3-phase capacitor is used to improve the power factor to unity. The capacitance power phase of...
For a single phase overhead line having solid copper conductors of diameter $$1$$ cm, spaced $$60$$ cm between centers, the inductance in $$mH/km$$ is
The enhancement type n-channel MOSFET is represented by the symbol
The $$RMS$$ value of half $$-$$ wave rectified symmetrical square wave current of $$2A$$ is
Two single phase transformers $$A$$ and $$B$$ have the following parameters. Transformer $$A$$: $$400V/200V,$$ $$10$$ $$kVA,$$ percentage resistance and percentage reactance are $$...
Resonant Converter's are basically used to
A three phase diode bridge is used to provide rectified output from a $$400V,$$ $$50$$ $$Hz,$$ $$3$$- phase supply to a $$R$$ $$-$$ $$L$$ load with $$10\,\,\Omega $$ resistance and...
When a resistor $$R$$ is connected to a current source, it consumes a power of $$18$$ $$W.$$ when the same $$R$$ is connected to a voltage source having the same magnitude as the c...
If $$A = \left[ {\matrix{ 1 & { - 2} & { - 1} \cr 2 & 3 & 1 \cr 0 & 5 & { - 2} \cr } } \right]$$ and $$adj (A)$$ $$ = \left[ {\matrix{ { - 11} & { - 9} & 1 \cr 4 & { - 2} & { - 3}...
For a dual $$ADC$$ type $$3\,{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$ digit $$DVM$$, the reference voltage is $$100$$ $$m...
A rectangular voltage pulse of magnitude $$V$$ and duration $$T$$ is applied to a series combination of resistance $$R$$ and capacitance $$C.$$ The maximum voltage developed across...
An overhead line having a surge impedance of $$400$$$$\Omega $$ is connected in series with an underground cable having a surge impedance of $$100$$$$\Omega $$. If a surge of $$50$...
Steady state stability of a power system is the ability of the power system to
A 6.6 kV, 50 Hz single core lead sheathed cable has the following data: Conductor diameter: 1.5 cm, length: 4 km. Internal diameter of the sheath : 3 cm Resistivity of insulation :...
A rectangular current pulse of duration T and magnitude 1 has the Laplace transform
Electro dynamic type watt meters have large errors while measuring power in a.c circuits at low power factor conditions, since the voltage across and the current though the
The voltage phasor of a circuit is $$10\angle {15^ \circ }V$$ and the current phasor is $$2\angle - {45^ \circ }A.$$ The active and the reactive powers in the circuit are
Two $$100$$ $$\mu A$$ full scale $$PMMC$$ meters are employed to construct a $$10$$ $$V$$ and a $$100$$ $$V$$ full scale voltmeter. These meters will have figures of merit (sensiti...
A current of $$\left[ {2 + \sqrt 2 \sin \left( {314t + 30} \right) + 2\sqrt 2 \cos \left( {952t + 45} \right)} \right]$$ is measured with a thermocouple type. $$5A$$ full scale, cl...
For a dual $$ADC$$ type $$3\,\,{1 \over 2}$$ digit $$DVM$$, the reference voltage is $$100mV$$ and the first integration time is set to $$300$$$$ms$$. For some input voltage, the '...