GATE 2002 Electrical Engineering

The determinant of the matrix $$\left[ {\matrix{ 1 & 0 & 0 & 0 \cr {100} & 1 & 0 & 0 \cr {100} & {200} & 1 & 0 \cr {100} & {200} & {300} & 1 \cr } } \right]$$ is

In a single phase $$3$$ winding transformer the turns ratio for primary: secondary: tertiary windings is $$20:4:1.$$ With the lagging currents of $$50A$$ at a power factor of $$0.6...

Consider a power system with three identical generators. The transmission losses are negligible. One generator ($$G1$$) has a speed governor which maintains its speed constant at t...

A 200 V, 2000 rpm, 10A, separately excited d.c. motor has an armature resistance of 2 $$\Omega$$. Rated d.c. voltage is applied to both the armature and field winding of the motor....

A 1 kVA, 230V/100V, single phase, 50 Hz transformer having negligible winding resistance and leakage inductance is operating under saturation, while 250 V, 50 Hz sinusoidal supply...

If a 400 V, 50 Hz, star connected, 3 phase squirrel cage induction motor is operated from a 400 V, 75 Hz supply, the torque that the motor can now provide while drawing rated curre...

The state transition matrix for the system $$\mathop X\limits^ \bullet = AX\,\,$$ with initial state $$X(0)$$ is

A transmission line has a total series reactance of 0.2 pu. Reactive power compensation is applied at the midpoint of the line and it is controlled such that the midpoint voltage o...

Given a vector field $$\overrightarrow F ,$$ the divergence theorem states that

Let $$Y(s)$$ be the Laplace transform of function $$y(t),$$ then the final value of the function is __________.

For the system $$X = \left[ {\matrix{ 2 & 3 \cr 0 & 5 \cr } } \right]X + \left[ {\matrix{ 1 \cr 0 \cr } } \right]u,$$ Which of the following statement is true?

Consider a long, two-wire line composed of solid round conductors. The radius of both conductors is $$0.25$$ cm and the distance between their centers is $$1$$m. If this distance i...

Given a vector field $${\overrightarrow F ,}$$ the divergence theorem states that

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 $$415$$ $$V,$$ $$2$$ pole, $$3$$ phase, $$50$$ $$Hz,$$ star connected, non-salient pole synchronous motor has synchronous reactance of $$2\,\Omega $$ per phase and negligible sta...

When a program is being executed in an $$8085$$ microprocessor, its Program Counter contains

A long wire composed of a smooth round conductor runs above and parallel to the ground (assumed to be a large conducting plane). A high voltage exists between the conductor and the...

For the system $$\mathop X\limits^ \bullet = \left[ {\matrix{ 2 & 0 \cr 0 & 4 \cr } } \right]X + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u;\,\,\,y = \left[ {\matrix{ 4 & 0 \cr } }...

The open loop transfer function of a unity feedback system is given by $$G\left( s \right) = {{2\left( {s + \alpha } \right)} \over {s\left( {s + 2} \right)\left( {s + 10} \right)}...

The transfer function of the system described by $${{{d^2}y} \over {d{t^2}}} + {{dy} \over {dt}} = {{du} \over {dt}} + 2u$$ with $$u$$ as input and $$y$$ as output 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...

A step down chopper is operated in the continuous conduction mode in steady state with a constant duty ratio $$D.$$ If $${V_0}$$ is the magnitude of the $$dc$$ output voltage and i...

The flux per pole in a synchronous motor with the field circuit ON and the stator disconnected from the supply is found to be $$25$$ $$mWb.$$ When the stator is connected to the ra...

A diode whose terminal characteristics are related as $${i_D} = {{\rm I}_S}\,{e^{{V \over {{V_T}}}}},\,$$ where $${{\rm I}_S}$$ is the reverse saturation current and $${V_T}$$ is t...

A unity feedback system has an open loop transfer function, $$G\left( s \right) = {K \over {{s^2}}}.$$ The root locus plot is

A $$230V,$$ $$250$$ $$rpm.$$ $$100A$$ separately excited $$dc$$ motor has an armature resistance of $$0.5\,\Omega .$$ The motor is connected to $$230V$$ $$dc$$ supply and rated $$d...

A three phase thyristor bridge rectifier is used in a $$HVDC$$ link. The firing angle $$\alpha $$ (as measured from the point of natural commutation) is constrained to lie between...

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 six pulse thyristor rectifier bridge is connected to a balanced $$50Hz$$ three phase $$ac$$ source. Assuming that the $$dc$$ output current of the rectifier is constant, the lowe...

Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is

$$s(t)$$ is step response and $$h(t)$$ is impulse response of a system. Its response $$y(t)$$ for any input $$u(t)$$ is given by

Kelvin double bridge is best suited for the measurement of

Two in-phase, 50Hz sinusoidal waveform of unit amplitude are fed into channel-1. and channel-2 respectively of an oscilloscope, Assuming that the voltage scale, time scale and othe...

A single input single output system with $$y$$ as output and $$u$$ as input, is described by $$${{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + 10y = 5{{d\,u} \over {dt}} - 3\,u$$...