# Electrical Engineering - GATE 2010 Paper Solution

The value of the quantity P, where P=$\int\limits_0^1xe^x\;dx$ is equal to

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Divergence of the three-dimensional radial vector field $\stackrel{\to }{r}$ is

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The period of the signal $x\left(t\right)=8\mathrm{sin}\left(0.8\mathrm{\pi }t+\frac{\mathrm{\pi }}{4}\right)\phantom{\rule{0ex}{0ex}}$ is

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The system represented by the input-output relationship $\style{font-size:14px}{y\left(t\right)=\int\limits_{-\infty}^{5t}x\left(\tau\right)d\tau,t>0}$ is

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The switch in the circuit has been closed for a long time. It is opened at t = 0. At t = 0+, the current through the 1μF capacitor is

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The second harmonic component of the periodic waveform given in the figure has an amplitude of

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As shown in the figure, a 1Ω resistance is connected across a source that has a load line v+ i = 100. The current through the resistance is

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A wattmeter is connected as shown in the figure. The wattmeter reads

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An ammeter has a current range of 0 - 5 A, and its internal resistance is 0.2Ω. In order to change the range to 0 - 25 A, we need to add a resistance of

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As shown in the figure, a negative feedback system has an amplifier of gain 100 with ±10% tolerance in the forward path, and an attenuator of value 9/100 in the feedback path. The overall system gain is approximately

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For the system $2}{\left(s+1\right)}\phantom{\rule{0ex}{0ex}}$ the approximate time taken for a step response to reach 98% of its final value is

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If the electrical circuit of figure (b) is an equivalent of the coupled tank system of figure (a), then

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A single-phase transformer has a turns ratio of 1:2, and is connected to a purely resistive load as shown in the figure. The magnetizing current drawn is 1A, and the secondary current is 1A. If core losses and leakage reactances are neglected, the primary current is

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Power is transferred from system A to system B by an HVDC link as shown in the figure. If the voltages VAB and VCD are as indicated in the figure, and I > 0, then

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A balanced three-phase voltage is applied to a star-connected induction motor, the phase to neutral voltage being V. The stator resistance, rotor resistance referred to the stator, stator leakage reactance, rotor leakage reactance referred to the stator, and the magnetizing reactance are denoted by rs, rr, xs , xr and Xm , respectively. The magnitude of the starting current of the motor is given by

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Consider a step voltage wave of magnitude 1pu travelling along a lossless transmission line that terminates in a reactor. The voltage magnitude across the reactor at the instant the travelling wave reaches the reactor is

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Consider two buses connected by an impedance of (0+j5) Ω. The bus 1 voltage is $100\angle 30°$V, and bus 2 voltage is 100∠ 0o$100\angle 0°$V.The real and reactive power supplied by bus 1, respectively, are

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A three-phase, 33kV oil circuit breaker is rated 1200A, 2000MVA, 3s. The symmetrical breaking current is

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Consider a stator winding of an alternator with an internal high-resistance ground fault. The currents under the fault condition are as shown in the figure. The winding is protected using a differential current scheme with current transformers of ratio 400/5 A as shown. The current through the operating coil is

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The zero-sequence circuit of the three phase transformer shown in the figure is