Thyristor  is triggered at an angle  (in degree), and  at angle 180° + α, in each cycle of the sinusoidal input voltage. Assume both thyristors to be ideal. To control the load power over the range 0 to 2 kW, the minimum range of variation in  is:

A common-source amplifier with a drain resistance, , is powered using a 10 V power supply. Assuming that the transconductance, gm is , the voltage gain of the amplifier is closest to:

The cross-section of a metal-oxide-semiconductor structure is shown schematically. Starting from an uncharged condition, a bias of +3 V is applied to the gate contact with respect to the body contact. The charge inside the silicon dioxide layer is then measured to be +Q. The total charge contained within the dashed box shown, upon

application of bias, expressed as a multiple of Q (absolute value in Coulombs, rounded off to the nearest integer) is ___________.

A non-ideal Si-based pn junction diode is tested by sweeping the bias applied across its terminals from –5 V to +5 V. The effective thermal voltage, , for the diode is measured to be (29 ± 2) mV. The resolution of the voltage source in the measurement range is 1 mV. The percentage uncertainty (rounded off to 2 decimal places) in the measured current at a bias voltage of 0.02 V is _______.

The temperature of the coolant oil bath for a transformer is monitored using the circuit shown. It contains a thermistor with a temperature-dependent resistance, , where T is the temperature in °C. The temperature coefficient, , is – (4 ± 0.25) %/°C. Circuit parameters: , , . The error in the output signal (in V, rounded off to 2 decimal places) at 150°C is __________.

Consider a signal , where u[n] = 0 if n < 0, and u[n] = 1 if n ≥ 0. The z-transform x[n – k], k > 0 is  with region of convergence being

Consider the initial value problem below. The value of  at . (rounded off to 3 decimal places) is __________.

The value of the following complex integral, with  representing the unit circle centered at origin in the counterclockwise sense, is

 and  are, respectively, the rms and average values of x(t) = x(t — T) , and similarly,  and  are, respectively, the rms and average values of . k,T are independent of t . Which of the following is true?

Which of the following is true for all possible non-zero choices of integers m, n; m ≠ n, or all possible non-zero choices of real numbers p, q; p ≠ q as applicable?

Which of the following statements is true about the two sided Laplace transform?

The causal realization of a system transfer function H(s) having poles at (2, –1), (–2,1) and zeroes at (2,1), (–2, –1) will be

Which of the options is an equivalent representation of the signal flow graph shown here?

The Thevenin equivalent voltage, , in V (rounded off to 2 decimal places) of the network shown below, is

A benchtop DC power supply acts as an ideal 4 A current source as long as its terminal voltage is below 10 V. Beyond this point, it begins to behave as an ideal 10 V voltage source for all load currents going down to 0A. When connected to an ideal rheostat, find the load resistance value at which maximum power is transferred, and the corresponding load voltage and current.  

Consider the diode circuit shown below. The diodes D, obeys the current-voltage characteristic

where n>1, ,  is the voltage across the diode and  is the current through it. The circuit is biased so that voltage, V > 0 and current, I<0,  If you had to design this circuit to transfer maximum power from the current source  to a resistive load (not shown) at the output, what values  and  would you choose?

A non-ideal diode is biased with a voltage of –0.03 V, and a diode current of  is measured. The thermal voltage is 26 mV and the ideality factor for the diode is 15/13. The voltage, in V, at which the measured current increases to  is closest to:

Consider a linear time-invariant system whose input r(t) and output y(t) are related by the following differential equation:

The poles of this system are at

Which of the following option is correct for the system shown below?

Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) * h(t) = y(t). Further, if |x(t)|*|h(t)| = z(t), which of the following statements is true?

A sequence detector is designed to detect precisely 3 digital inputs, with overlapping sequences detectable. For the sequence (1,0,1) and input data (1,1,0,1,0,0,1,1,0,1,0,1,1,0), what is the output of this detector?

Consider a negative unity feedback system with the forward path transfer function , where K is a positive real number. The value of K for which the

system will have some of its poles on the imaginary axis is

Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:                

An 8085 microprocessor accesses two memory locations (2001H) and (2002H), that contain 8-bit numbers 98H and B1H, respectively. The following program is executed:

LXI H,2001H

MVI A, 21H

INXH

ADD M

INXH

MOV M, A

HLT

At the end of this program, the memory location 2003H contains the number in decimal (base 10) form.         

Out of the following options, the most relevant information needed to specify the real power (P) at the PV buses in a load flow analysis is

A single-phase inverter is fed from a 100 V dc source and is controlled using a quasi-square wave modulation scheme to produce an output waveform, v(t) as shown. The angle σ is adjusted to entirely eliminate the  harmonic component from the output voltage. Under this condition for v(t), the magnitude of the  harmonic component as a percentage of the magnitude of the fundamental component is _________. (rounded off to 2 decimal places).

Two buses, i and j, are connected with a transmission line of admittance Y, at the two ends of which there are ideal transformers with turns ratios as shown. Bus admittance matrix for the system is:

A conducting square loop of side length 1 m is placed at a distance of 1 m from a long straight wire carrying a current I = 2 A as shown below. The mutual inductance, in nH (rounded off to 2 decimal places), between the conducting loop and the long wire is __________.

A resistor and a capacitor are connected in series to a 10 V DC supply through a switch. The switch is closed at t=0, and the capacitor voltage is found to cross 0V at t=0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossing has to happen at t=0.2τ is_________ (rounded off to 2 decimal places).

A double pulse measurement for an inductively loaded circuit controlled by the IGBT switch is carried out to evaluate the reverse recovery characteristics of the diode. D, represented approximately as a piecewise linear plot of current vs time at diode turn-off.  is a parasitic inductance due to the wiring of the circuit, and is in series with the diode. The point on the plot (indicate your choice by entering 1, 2, 3 or 4) at which the IGBT experiences the highest current stress is

In the DC-DC converter circuit shown, switch Q is switched at a frequency of 10 kHz with a duty ratio of 0.6. All components of the circuit are ideal, and the initial current in the inductor is zero. Energy stored in the inductor in mJ (rounded off to 2 decimal places) at the end of 10 complete switching cycles is _________.

 is a polynomial on real  over real coefficients  wherein. Which of the following statements is true?

For real numbers,  and  with , the maximum and minimum value of  for  are respectively _________.

Let  and  be unit vectors along  and  directions, respectively. A vector function is given by .

The line integral of the above function,  along the curve , which follows the parabola  as shown below is __________. (rounded off to 2 decimal places).         

Consider a negative unity feedback system with forward path transfer function  where K, a, b, c are positive real numbers. For a Nyquist path enclosing the entire imaginary axis and right half of the s-plane in the clockwise direction, the Nyquist plot of (l + G(s)), encircles the origin of (l + G(s))-plane once in the clockwise direction and never passes through this origin for a certain value of K. Then, the number of poles of lying in the open right half of the s-plane is _______.

Consider a permanent magnet dc (PMDC) motor which is initially at rest. At t = 0, a dc voltage of 5 V is applied to the motor. Its speed monotonically increases from 0 rad/s to 6.32 rad/s in 0.5 s and finally settles to 10 rad/s. Assuming that the armature inductance of the motor is negligible, the transfer function for the motor is

A stable real linear time-invariant system with single pole at p, has a transfer function  with a dc gain of 5. The smallest positive frequency, in rad/s, at unity gain is closest to:

The vector function expressed by

represents a conservative field, where , ,  are unit vector along x, y and z directions, respectively. The values of constants , ,  are given by:

The static electric field inside a dielectric medium with relative permittivity, , expressed in cylindrical coordinate system is given by the following expression

where , ,  are unit vectors along r,  and z directions, respectively. If the above expression represents a valid electrostatic field inside the medium, then the volume charge density associated with this field in terms of free space permittivity, , in SI units is given by:

Let ,  and  be unit vectors along r,  and z directions, respectively in the cylindrical coordinate system. For the electric flux density given by  , the total electric flux, in Coulomb, emanating from the volume enclosed by a solid cylinder of radius 3 m and height 5 m oriented along the z-axis with its base at the origin is:

The number of purely real elements in a lower triangular representation of the given  matrix, obtained through the given decomposition is

Current through ammeters  and  in fig. are 1 ∠ 10° and 1 ∠ 70° respectively. The reading of the ammeter A1 (rounded off to 3 decimal places) is _________ A.

A single-phase, full-bridge diode rectifier fed from a 230 V, 50 Hz sinusoidal source supplies a series combination of finite resistance. R, and a very large inductance, L. The two most dominant frequency components in the source current are:

A three-phase cylindrical rotor synchronous generator has a synchronous reactance  and a negligible armature resistance. The magnitude of per phase terminal voltage is and the magnitude of per phase induced emf is . Considering the following two statements, P and Q,

P: For any three phase balanced leading load connected across the terminals of this synchronous generator,  is always more than  

Q: For any three-phase balanced lagging load connected across the terminals of this synchronous generator, is always less than  

Which of the following options is correct?

A single-phase, full-bridge, fully controlled thyristor rectifier feeds a load comprising a 10 Ω resistance in series with a very large inductance. The rectifier is fed from an ideal 230 V, 50 Hz sinusoidal source through cables which have negligible internal resistance and a total inductance of 2.28 mH. If the thyristors are triggered at an angle , the commutation overlap angle in degree (rounded off to 2 decimal places) is ______.

A single 50 Hz synchronous generator on droop control was delivering 100 MW power to a system. Due to increase in load, generator power had to be increased by 10 MW, as a result of which, system frequency dropped to 49.75 Hz. Further increase in load in the system resulted in a frequency of 49.25 Hz. At this condition, the power in MW supplied by the generator is __________ (rounded off to 2 decimal pages).

A 250 V DC shunt motor has an armature resistance of 0.2 Ω and a field resistance of 100 Ω. When the motor is operated on no-load at rated voltage. It draws an armature current of 5 A and runs at 1200 rpm. When a load is coupled to the motor, it draws total line current of 50 A at rated voltage, with a 5 % reduction in the air-gap flux due to armature reaction. Voltage drop across the brushes can be taken as 1 V per brush under all operating conditions. The speed of the motor, in rpm, under this loaded condition, is closest to:

The figure below shows the per-phase Open Circuit Characteristics (measured in V) and Short Circuit Characteristics (measured in A) of a 14 kVA, 400~V. 50~Hz, 4-pole, 3-phase, delta connected alternator, driven at 1500 rpm. The field current, If is measured in A. Readings taken are marked as respective (x, y) coordinates in the figure. Ratio of the unsaturated and saturated synchronous impedances  of the alternator is closest to

A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current to a 0.9 lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the total lagging reactive power requirement of the load is twice the previous value while the real power remains unchanged. The armature current is now _________ A (Rounded off to 2 decimal places).

A cylindrical rotor synchronous generator has steady state synchronous reactance of 0.7 pu and subtransient reactance of 0.2 pu. It is operating at (1 + j0) pu terminal voltage with an internal emf of (1 + j0.7) pu. Following a three-phase solid short circuit fault at the terminal of the generator, the magnitude of the subtransient internal emf (rounded off to 2 decimal places) is _____________ pu.

A three-phase, 50 Hz, 4-pole induction motor runs at no-load with a slip of 1 %. With full load, the slip increases to 5 %. The % speed regulation of the motor (rounded off to 2 decimal places) is

A single-phase, 4 kVA, 200 V/100 V, 50 ~Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal AC supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal AC source, the no-load losses will be …………… W (rounded off to 2 decimal places).

Windings 'A', 'B' and 'C' have 20 turns each and are wound on the same iron core as shown, along with winding 'X which has 2 turns. The figure shows the sense (clockwise/anti-clockwise) of each of the windings only and does not reflect the exact number of turns, If windings 'A', 'B' and 'C' are supplied with balanced 3 -phase voltages at 50 Hz and there is no core saturation, the no-load RMS voltage (in V, rounded off to 2 decimal places) across winding ' X is ____________

A lossless transmission line with 0.2 pu reactance per phase uniformly distributed along the length of the line, connecting a generator bus to a load bus, is protected up to 80 % of its length by a distance relay placed at the generator bus. The generator terminal voltage is 1 pu. There is no generation at the load bus. The threshold pu current for operation of the distance relay for a solid three phase-to-ground fault on the transmission line is closest to:

Bus 1 with voltage magnitude  is sending reactive power  towards bus 2 with voltage magnitude  through a lossless transmission line of reactance X. Keeping the voltage at bus 2 fixed at 1 pu, magnitude of voltage at bus 1 is changed, so that the reactive power  sent from bus 1 is increased by

20%. Real power flow through the line under both the conditions is zero. The new value of the voltage magnitude, , in pu (rounded off to 2 decimal places), at bus 1 is __________.