Two identical coils are each having inductance L are placed together on the some core. If an overall inductance of  is obtained by interconnecting these two coils, the minimum value of  is _______________.

A capacitive voltage divider is used to measure the bus voltage  in a high-voltage 50Hz AC system as shown in figure. The measurement capacitors  and  have tolerance of  on their nominal capacitance values. If the bus voltage  is 100kV rms, the maximum rms output voltage (in kV), considering the capacitance tolerances, is _________

A differential equation  is applicable over – 10 < t < 10. If , then i(-5) is ___________.

The incremental costs (in Rupees/MWh) of operating two generating units are functions of their respective powers  and  in MW, are given by         

where,   

For a certain load demand, and  have been chosen such that Rs/MWh and Rs/MWh. If the generations are rescheduled to minimize the total cost, then  is__________.

The filters F1 and F2 having characteristics as shown in figures (a) and (b) are connected as shown in figure (c)

The cut – off frequencies of F1 and F2 are  and  respectively. If , the resultant circuit exhibit the characteristics of a

Consider a signal defined by

Its Fourier Transform is

An open loop transfer function G(s) of a system is  

For a unity feedback system, the breakaway point of the root on the real axis occurs at,

The Laplace transform of  is . The Laplace transform of  is

Two coins R and S are tossed. The 4 joint events  have probabilities 0.28, 0.18, 0.30, 0.24, respectively, where H represents head and T represents tail. Which one of the following is TRUE?

For linear time invariant systems, that are Bounded input Bounded output stable, which one of the following statements is TRUE?

The z – transform of a sequence  is given as. If y[n] is the first difference of x[n], then Y(z) is given by

Consider the following sum of products expression, F.

The equivalent product of sums expressions is

The current i(in Ampere) in the  resistor of the given network is _______.

A Boolean function  is to be implemented using an 8 x 1 multiplexer (A is MSB), The inputs ABC are connected to the select inputs  of the multiplexer respectively.

Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order?

In the following circuit, the input voltage  is 100. For , the average voltage across R (in volts) under steady – state is nearest to

A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is

If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the  row  column element (in pu) of the bus admittance matrix after compensation is

In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is . The state , immediately after the 333rd clock pulse is

The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude E are constant. If one line is tripped at time  by opening the circuit breakers at the two ends (although there is no fault), then it is seen that the generator undergoes a stable transient. Which one of the following waveforms of the rotor angle  shows the transient correctly?

A circular turn of radius 1m revolves at 60rpm about its diameter aligned with the x – axis as shown in the figure. The value of  is  is SI unit. If a uniform magnetic field intensity  A/m is applied, then the peak value of induced voltage, (in Volts), is _____________.

Given , where f, g, h are complex valued functions of a complex variable z. Which one of the following statements is TRUE?

A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero initial conditions, the value of  at t = 0 is

The volume enclosed by the surface  over the triangle bounded by the lines    x = y; x = 0; y = 1 in the xy plane is _________.

The following discrete – time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variable x and y. The integration time step is h.         

For this discrete – time system, which one of the following statements is TRUE?

A buck converter feeding a variable load is shown in the figure. The switching frequency of the switch is 100 kHz and the duty ratio is 0.6. The output voltage  is 36 V. Assume that all the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that will make the inductor current () just continuous is __________.

In the following circuit, the transistor is in active mode and . To get , we replace  with . Then the ratio  is _______________.

For the system governed by the set of equations: 

the transfer function Y(s)/U(s) is given by

A 3-phase transformer rated for 33 kV/11kV is connected in delta/star as shown in figure. The current transformers (CTs) on low and high voltage sides has a ratio of 500/5. Find the currents  and, if the fault current is 300 A as shown in figure.

For switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positive and continuous and switching period is. If the voltage is as shown, the duty cycle of the switch S is______.

When a bipolar junction transistor is operating in the saturation mode, which one of the following statements is TRUE about the state of its collector – base (CB) and the base – emitter (BE) junctions?

Match the following:

Two semi – infinite dielectric regions are separated by a plane boundary at y = 0. The dielectric constants of region 1 (y < 0) and region 2(y > 0) are 2 and 5, respectively. Region 1 has uniform electric field  where and  are unit vectors along the x, y and z axes, respectively. The electric field in region 2 is

Nyquist plots of two functions  and  are shown in figure. 

Nyquist plot of the product of  is

An open loop control system results in a response of  for a unit impulse input. The DC gain of the control system is ___________.

Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +Q is placed at a distance of d from both sheets. The net force on the charge is, where K is given by

The unit step response of a system with the transfer function  is given by which one of the following waveforms?

We have a set of 3 linear equations in 3 unknowns. ‘X = Y’ means X and Y are equivalent statements and  means X and Y are not equivalent statements.

P. There is a unique solution.

Q. The equations are linearly independent.

R. All Eigen values of the coefficient matrix are nonzero.

S. The determinant of the coefficient matrix is nonzero.

Which one of the following is TRUE?

In the given rectifier, the delay angle of the thyristor  measured from the positive going zero crossing of  is . If the input voltage is  V, the average voltage across R (in Volt) under steady-state is __________.

In the given network. , ,  

The phasor current i (in Ampere) is

A symmetrical square wave of 50% duty cycle has amplitude of ±15V and time period of . This square wave is applied across a series RLC circuit with  L=10mH and . The amplitude of the 5000 rad/s component of the capacitor voltage (in volt) is ____________.          

A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200 radian/sec. At its rated torque of 500 Nm, its speed is 180 radian/sec. The motor is used to directly drive a load whose load torque  depends on its rotational speed  (in radian/second), such that . Neglecting rotational losses, the steady-state speed (in radian/second ) of the motor, when it drives this load, is_________.

A three-phase, 11 kV, 50 Hz, 2pole, star connected, and cylindrical rotor synchronous motor is connected to an 11kV, 50 Hz source. Its synchronous reactance is  per phase, and its stator resistance is negligible. The motor has a constant field excitation. At a particular load torque, its stator current is 100A at unity power factor. If the load torque is increased so that the stator current is 120 A, then the load angle (in degrees) at this load is __________.

A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated for 230V and 5kW at a speed of 1200 rpm. If the same armature coils are reconnected to form a lap winding, what is rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the reconnected machine if the field circuit is left unchanged?

The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is , The amplitude of the output voltage  (in Volt) is____________.        

With an armature voltage of 100 V and rated field winding voltage, the speed of a separately excited DC motor driving a fan is 1000rpm, and its armature current is 10 A. The armature resistance is 1 . The load torque of the fan load is proportional to the square of the rotor speed. Neglecting rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor speed to 500rpm is ___________________.

The saturation voltage of the ideal op – amp shown below is ±10V. The output voltage  of the following circuit in the steady – state is

Match the following. 

(A)        (B)        (C)        (D)

P-1        P-1          P-1          P-3

Q-2         Q-3          Q-2          Q-1

R-1         R-1          R-3          R-2

S-3         S-2         S-3          S-1

A 3-phase balanced load which has a power factor of 0.707 is connected to a balanced supply. The power consumed by the load is 5kW. The power is measured by the two-wattmeter method. The reading of the two watt meters are

The coils of a wattmeter have resistance 0.01 and 1000; their inductances may be neglected. The wattmeter is connected as shown in the figure, to measure the power consumed by a load, which draws 25 A at power factor 0.8. The voltage across the load terminals is 30 V. The percentage error on the wattmeter reading is __________.

The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at 50 Hz. The “air-gap” voltage,  across the magnetizing inductance, is 210 V rms, and the slip, s, is 0.05. The torque (in Nm) produced by the motor is __________.

A 220 V, 3-phase, 4-pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The maximum torque produced by the rotor is 225% of full load torque and it occurs at 15% slip. The actual rotor resistance is 0.03. The value of external resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is______.

Find the transformer ratios a and b such that the impedance ( ) is resistive and equals  when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.

A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, star connected load through a star-delta transformer as shown in the figure. The line-to-line voltage rating is 230 V on the star side, and 115 V on the delta side. If the magnetizing current is neglected and  A, then what is the value of  in Ampere?

A three-winding transformer is connected to an AC voltage source as shown in the figure. The number of turns are as follows: . If the magnetizing current is neglected, and the currents in two windings are  = and =  A, then what is the value of the current  in Ampere?

Two three-phase transformers are realized using single-phase transformers as shown in the figure.

The phase difference (in degree) between voltages  and  is ___________.

A composite conductor consists of three conductors of radius R each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR.  The value of k is ____________.