GATE 2007 Electrical Engineering

A $$100$$ $$kVA$$, $$415V,$$ star connected synchronous machine generates rated open circuit voltage $$415V$$ at a field current of $$15A.$$ The short circuit armature current at a...

Which one of the following statements regarding the $$INT$$ (interrupt) and the $$BRQ$$ (bus request) pins in a $$CPU$$ is true?

Divergence of the vector field $$$\overrightarrow V\left(x,y,z\right)=-\left(x\cos xy\;+\;y\right)\;\widehat i\;+\;\left(y\cos xy\right)\;\widehat j\;+\;\left(\sin\;z^2\;+\;x^2\;+\...

In a transformer, zero voltage regulation at full load is

A single $$-$$ phase fully controlled thyristor bridge $$ac$$ $$-$$ $$dc$$ converter is operating at a firing angle of $${25^ \circ }$$ and an overlap angle of $${10^ \circ }$$ con...

Divergence of the vector field $$v\left( {x,y,z} \right) = - \left( {x\,\cos xy + y} \right)\widehat i + \left( {y\,\cos xy} \right)\widehat j + \left[ {\left( {\sin {z^2}} \right)...

The system $$900/s(s+1)(s+9)$$ is to be such that its gain crossover frequency becomes same as its uncompensated phase crossover frequency and provides at $${45^0}$$ phase margin ....

The integral $$\,\,{1 \over {2\pi }}\int\limits_0^{2\Pi } {Sin\left( {t - \tau } \right)\cos \tau \,d\tau \,\,\,} $$ equals

A $$1:1$$ pulse transformer $$(PT)$$ is used to trigger the $$SCR$$ in the adjacent figure. The $$SCR$$ is rated at $$1.5$$ $$kV$$, $$250$$ $$A$$ with $${{\rm I}_L} = 250\,mA,\,\,{...

A single - phase voltage source inverter is controlled in a single pulse - width modulated mode with a pulse width of $${150^0}$$ in each half cycle. Total harmonic distortion is d...

The dc motor, which can provide zero speed regulation at full load without any controller is

If $$A = \left[ {\matrix{ { - 3} & 2 \cr { - 1} & 0 \cr } } \right]$$ then $$A$$ satisfies the relation

The matrix $$A$$ given below is the node incidence matrix of a network. The columns correspond to braches of the network while the rows correspond to nodes. Let $$V = {\left[ {{v_1...

If the loop gain $$K$$ of a negative feedback system having a loop transfer function $$K\left( {s + 3} \right)/{\left( {s + 8} \right)^2}$$ is to be adjusted to induce a sustained...

A three - phase fully - controlled thyristor bridge converter is used as line commuted inverter to feed $$50kW$$ power $$420$$ $$V$$ $$dc$$ to a three phase, $$415$$ $$V$$ (line),...

If $$X = {\mathop{\rm Re}\nolimits} G\left( {j\omega } \right),\,\,$$ and $$y = {\rm I}mG\left( {j\omega } \right)$$ then for $$\omega \to {0^ + },\,\,$$ the Nyquist plot for $$G\l...

In an $$8085$$ $$A$$ microprocessor based system, it is desired to increment the contents of memory location whose address is available in $$(D,E)$$ register pair and store the res...

Let $$x$$ and $$y$$ be two vectors in a $$3-$$ dimensional space and $$ < x,y > $$ denote their dot product. Then the determinant det $$\left[ {\matrix{ { < x,x > } & { < x,y > } \...

Suppose we define a sequence transformation between ''a-b-c'' and ''p-n-0''' variables as follows: $$\left[ {\matrix{ {{f_a}} \cr {{f_b}} \cr {{f_c}} \cr } } \right] = k\left[ {\ma...

A three-phase squirrel cage induction motor has a starting torque of $$150\% $$ and a maximum torque of $$300\% $$ with respect to rated torque at rated voltage and rated frequency...

A three phase squirrel cage induction motor has a starting current of seven times the full load current and full load slip of $$5\% $$ If an auto-transformer is used for reduced vo...

$$X = {\left[ {\matrix{ {{x_1}} & {{x_2}} & {.......\,{x_n}} \cr } } \right]^T}$$ is an $$n$$-tuple non- zero vector. The $$n\,\, \times \,\,n$$ matrix $$V = X{X^T}$$

An inductor designed with $$400$$ turns coil wound on an iron core of $$16\,\,c{m^2}$$ cross sectional area and with a cut of an air gap length of $$1$$ $$mm$$. The coil is connect...

A three phase synchronous motor connected to ac mains is running at full load and unity power factor. If its shaft load is reduced by half, with field current held constant, its ne...

An inductor designed with $$400$$ turns coil wound on an iron core of $$16\,\,c{m^2}$$ cross sectional area and with a cut of an air gap length of $$1$$ $$mm$$. The coil is connect...

If $$A = \left[ {\matrix{ { - 3} & 2 \cr { - 1} & 0 \cr } } \right]\,$$ then $${A^9}$$ equals

A $$3$$ phase, $$3$$ stack, variable reluctance stepper motor has $$20$$ poles on each rotor and stator stack. The step angle of this stepper motor is

A $$3$$ $$V$$ $$dc$$ supply with an internal resistance of $$2$$ $$\Omega $$ supplies a passive non-linear resistance characterized by the relation $${V_{NL}} = {{\rm I}^2}{}_{NL}$...

A three phase squirrel cage induction motor has a starting current of seven times the full load current and full load slip of $$5\% $$ If a star-delta starter is used to start this...

Consider the function $$f\left( x \right) = {\left( {{x^2} - 4} \right)^2}$$ where $$x$$ is a real number. Then the function has

A single phase full $$-$$ wave half $$-$$ controlled bridge converter feeds an inductive load. The two $$SCR's$$ in the converter are connected to a common $$DC$$ bus. The converte...

A three phase squirrel cage induction motor has a starting current of seven times the full load current and full load slip of $$5\% $$ If a starting torque of $$0.5$$ per unit is r...

A solid sphere made of insulating material has a radius $$R$$ and has a total charge $$Q$$ distributed uniformly in its volume. What is the magnitude of the electric field intensit...

''Six $$MOSFETS$$ connected in a bridge configuration (having no other power device) MUST be operated as Voltage Source Inverter $$(VSI)''.$$ This statement is

The total reactance and total susceptance of a lossless overhead $$EHV$$ line, operating at $$50$$ $$Hz,$$ are given by $$0.045$$ pu and $$1.2$$ pu respectively. If the velocity of...

$$230$$ $$V$$ (phase) $$50$$ Hz, three-phase, $$4$$-wire, system has a sequence $$ABC$$. A unity power-factor load of $$4$$ kW is connected between phase A and neutral $$N$$. It is...

A single $$-$$ phase, $$230$$ $$V$$, $$50$$ $$Hz$$ $$ac$$ mains fed step down transformer $$(4:1)$$ is supplying power to a half $$-$$ wave uncontrolled $$ac$$ $$-$$ $$dc$$ convert...

A single-phase $$50$$ $$kVA,$$ $$250$$ $$V/500V$$ two winding transformer has an efficiency of $$95\% $$ at full load, unity power factor. If it is reconfigured as a $$500V/750V$$...

A three phase balanced star connected voltage source with frequency $$\omega \,\,rad/s$$ is connected to a star connected balanced load which is purely inductive. The instantaneous...

$${q_1},\,{q_2},{q_3},.......{q_m}$$ are $$n$$-dimensional vectors with $$m < n.$$ This set of vectors is linearly dependent. $$Q$$ is the matrix with $${q_1},\,{q_2},{q_3},..........

If u(t), r(t) denote the unit step and unit ramp functions respectively and u(t)*r(t) their convolution, then the function u(t+1)*r(t-2) is given by

$$X\left( z \right) = 1 - 3\,\,{z^{ - 1}},\,\,Y\left( z \right) = 1 + 2\,\,{z^{ - 2}}$$ are $$Z$$-transforms of two signals $$x\left[ n \right],\,\,y\left[ n \right]$$ respectively...

A signal is processed by a causal filter with transfer function $$G(s).$$ For a distortion free output signal waveform, $$G(s)$$ must. $$G\left( z \right) = a{z^{ - 1}} + \beta \,\...

A signal $$x(t)$$ is given by $$x\left( t \right) = \left\{ {\matrix{ {1, - {\raise0.5ex\hbox{$\scriptstyle T$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}} < t \l...

Let a signal $${a_1}\,\sin \left( {{\omega _1}t + {\phi _1}} \right)$$ be applied to a stable linear time-invariant system. Let the corresponding steady state output be represented...

A $$3$$ $$V$$ $$dc$$ supply with an internal resistance of $$2\,\,\Omega $$ supplies a passive non-linear resistance characterized by the relation $${V_{NL}} = {\rm I}_{NL}^2.$$ Th...

A signal is processed by a causal filter with transfer function $$G(s).$$ For a distortion free output signal waveform, $$G(s)$$ must