# Electrical Engineering - GATE 2007 Paper Solution

The common emitter forward current gain of the transistor shown is ${\mathrm{\beta }}_{\mathrm{F}}$ = 100.

The transistor is operating in

The three-terminal linear voltage regulator is connected to a 10Ω load resistor as shown in the figure. If Vin is 10 V, what is the power dissipated in the transistor ?

Consider the transformer connections in a part of a power system shown in the figure. The nature of transformer connections and phase shifts are indicated for all but one transformer.

Which of the following connections, and the corresponding phase shift θ, should be used for the transformer between A and B?

The incremental cost curves in Rs/MWhr for two generators supplying a common load of 700 MW are shown in the figures. The maximum and minimum generation limits are also indicated. The optimum generation schedule is

Two regional systems, each having several synchronous generators and loads are inter connected by an ac line and a HVDC link as shown in the figure. Which of the following statements is true in the steady state:

Considered a bundled conductor of an overhead line consisting of three identical sub-conductors placed at the corners of an equilateral triangle as shown in the figure. If we neglect the charges on the other phase conductor and ground, and assume that spacing between sub-conductors is much larger than their radius, the maximum electric field intensity is experienced at

The circuit shown in the figure is

The system shown in the figure is

Let a signal $a_1\sin\left(\omega_1t+\phi_1\right)$ be applied to a stable linear time invariant system. Let the corresponding steady state output be represented as $a_2F\left(\omega_2t+\phi_2\right)$. Then which of the following statement is true?

The frequency spectrum of a signal is shown in the figure. If this signal is ideally sampled at intervals of 1 ms, then the frequency spectrum of the sampled signal will be

 (A) (B) (C) (D)

Divergence of the vector field V(x,y,z) = -(x cosxy+y)i + (y cosxy)j + (sin z2+x2+y2)k is

x = [x1 x2 ... xn]T is an n-tuple nonzero vector. The n×n matrix  V=xx T

A single-phase fully controlled thyristor bridge ac-dc converter is operating at a firing angle of 25° and an overlap angle of 10° with constant dc output current of 20 A. The fundamental power factor (displacement factor) at input ac mains is

A three-phase, fully controlled thyristor bridge converter is used as line commutated inverter to feed 50 kW power 420 V dc to a three-phase, 415 V(line), 50 Hz ac mains. Consider dc link current to be constant. The rms current of the thyristor is

In a transformer, zero voltage regulation at full load is

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

The probes of a non-isolated, two channel oscillocope are clipped to points A, B and C in the circuit of the adjacent figure. Vin is a square wave of a suitable low frequency. The display on Ch1 and Ch2 are as shown on the right. Then the “Signal” and “Ground” probes S1, G1 and S2, G2 of Ch1 and Ch2 respectively are connected to points: