GATE 2012 Electrical Engineering

The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$ The phase of the above lead compensator is maximum at

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

The output $$Y$$ of a $$2$$ $$-$$ bit comparator is logic $$1$$ whenever the $$2$$-bit input $$A$$ is greater than the $$2$$-bit input $$B.$$ The number of combination for which th...

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...

A 220 V, 15 kW, 1000 rpm shunt motor with armature resistance of 0.25 Ω , has a rated line current of 68 A and a rated field current of 2.2 A. The change in field flux required to...

A single phase 10 kVA, 50 Hz transformer with 1 kV primary winding draws 0.5 A and 55 W, at rated voltage and frequency, on no load. A second transformer has a core with all its li...

The slip of an induction motor normally does not depend on

The locked rotor current in a 3-phase, star connected 15 kW, 4-pole, 230 V, 50 Hz induction motor at rated conditions is 50 A. Neglecting losses and magnetizing current, the approx...

The typical ratio of latching current to holding current in a $$20$$ $$A$$ thyristor is

The maximum value of $$f\left( x \right) = {x^3} - 9{x^2} + 24x + 5$$ in the interval $$\left[ {1,6} \right]$$ is

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$ $${G_c}\left( s \right)$$ is a lead compensator if

A half-controlled single-phase bridge rectifier is supplying an $$R$$-$$L$$ load. It is operated at a firing angle $$α$$ and the load current is continuous. The fraction of cycle t...

Given that $$A = \left[ {\matrix{ { - 5} & { - 3} \cr 2 & 0 \cr } } \right]$$ and $${\rm I} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],$$ the value of $${A^3}$$ is

The unilateral Laplace transform of $$f(t)$$ is $$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$t$$ $$f(t)$$ is

With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\,\,\,$$ is

Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ The probability that max $$\left[ {X,Y} \right]$$ is less th...

The sequence components of the fault current are as follows: $${{\rm I}_{positive}} = j1.5\,pu,\,\,{{\rm I}_{negative}} = - j0.5\,\,pu,$$ $${{\rm I}_{zero}} = - j1\,\,pu.$$ The typ...

A cylindrical rotor generator delivers $$0.5$$ pu power in the steady-state to an infinite bus through a transmission line of reactance $$0.5$$ pu. The generator no-load voltage is...

The direction of vector $$A$$ is radially outward from the origin, with $$\left| A \right| = K\,{r^n}$$ where $${r^2} = {x^2} + {y^2} + {z^2}$$ and $$K$$ is constant. The value of...

Given $$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$ If $$C$$ is a counterclockwise path in the $$z$$-plane such that $$\left| {z + 1} \right| = 1,$$ the value of $...

The bus admittance matrix of a three-bus three-line system is $$y = j\left[ {\matrix{ { - 13} & {10} & 5 \cr {10} & { - 18} & {10} \cr 5 & {10} & { - 13} \cr } } \right]$$ If each...

A system with transfer function $$\,G\left( s \right) = {{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \right)\left( {s + 3} \right)\left( {s + 4} \right...

In the sum of products function $$f\,\left( {X,\,Y,\,Z} \right) = \sum \left( {2,\,\,3,\,\,4,\,\,5} \right),$$ the prime implicants are

If $$x = \sqrt { - 1} ,\,\,$$ then the value of $${X^x}$$ is

Consider the differential equation $${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$ with $$y\left( t...

If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then the region of convergence $$(ROC)$$ of its $$Z$$-transform...

L et y[n] denote the convolution of h[n] and g[n], where $$h\left[n\right]=\left(1/2\right)^nu\left[n\right]$$ and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1]...

The input x(t) and output y(t) of a system are related as $$\int_{-\infty}^tx\left(\tau\right)\cos\left(3\tau\right)d\tau$$.The system is

The Fourier transform of a signal h(t) is $$H\left(j\omega\right)=\left(2\cos\omega\right)\left(\sin2\omega\right)/\omega$$. The value of h(0) is

The unilateral Laplace transform of f(t) is $$\frac1{s^2\;+\;s\;+\;1}$$. The unilateral Laplace transform of tf(t) is

An analog voltmeter uses external multiplier settings. With a multiplier setting of $$20\,\,k\Omega ,$$ it reads $$440$$ $$V$$ and with a multiplier setting of $$80$$ $$k\Omega ,$$...

The bridge method commonly used for finding mutual inductance is