The line currents of a three-phase four wire system are square waves with amplitude of 100 A. These three currents are phase shifted by 120° with respect to each other. The rms value of neutral current is

Given  is the gate-source voltage,  is the drain source voltage, and  is the threshold voltage of an enhancement type NMOS transistor, the conditions for transistor to be biased in saturation are

The enhancement type MOSFET in the circuit below operates according to the square law. , the threshold voltage  is 500 mV. Ignore channel length modulation. The output voltage  is

A current controlled current source (CCCS) has an input impedance of  and output impedance of . When this CCCS is used in a negative feedback closed loop with a loop gain of 9, the closed loop output impedance is

The transfer function of a phase lead compensator is given by

The frequency (in rad/sec), at which  is maximum, is

The partial differential equation

 is known as

Which one of the following functions is analytic in the region ?

In the circuit shown below, X and Y are digital inputs, and Z is a digital output. The equivalent circuit is a

The closed loop line integral

evaluated counter-clockwise, is

A system transfer function is  . If  , and all other coefficients are positive, the transfer function represents a

A periodic function f(t), with a period of , is represented as its Fourier series,        

.

If

,

The Fourier series coefficients  and of f(t) are

The inverse Laplace transform of  

 is        

The mean-square of a zero-mean random process is  where k is Boltzmann’s constant, T is the absolute temperature, and C is a capacitance. The standard deviation of the random process is        

The probability of a resistor being defective is 0.02. there are 50 such resistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is ________.

The output expression for the Karnaugh map shown below is

The Symbols, a and T, represent positive quantities, and  is the unit step function. Which one of the following impulse responses is not the output of a causal linear time-invariant system?

The Characteristic equation of a linear time-invariant (LTI) system is given by

The system is BIBO stable if        

The  matrix of a two-bus power system having two identical parallel lines connected between them in pu is given as          

The magnitude of the series reactance of each line in pu (round off up to one decimal place) is ________________.

The output voltage of a single-phase full bridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms component of output voltage to be 75% of DC voltage, the required pulse width in degrees (round off up to one decimal place) is _____________.

The total impedance of the secondary winding, leads, and burden of a 5A CT is . If the fault current is 20 times the rated primary current of the CT, the VA output of the CT is_____________.

In a 132 kV system, the series inductance up to the point of circuit breaker location is 50 mH. The shunt capacitance at the circuit breaker terminal is 0.05. The critical value of resistance in ohms required to be connected across the circuit breaker contacts which will give no transient oscillation is __________.

In the circuit shown below, the switch is closed at t=0. The value of  in degrees which will give the maximum value of DC offset of the current at the time of switching is

A 0.1capacitor charged to 100 V is discharged through a resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to 1 V is ___________

Consider a state-variable model of a system

where y is the output, and r is the input. The damping ratio  and the undamped natural frequency  (rad/sec) of the system are given by

A DC-DC buck converter operates in continuous conduction mode. It has 48 V input voltage, and it feeds a resistive load of 24 Ω. The switching frequency of the converter is 250 Hz. If switch-on duration is 1 ms, the load power is

In a DC-DC boost converter, the duty ratio is controlled to regulate the output voltage at 48 V. The input DC voltage is 24 V. The output power is 120 W. The switching frequency is 50 kHz. Assume ideal components and a very larger output filter capacitor. The converter operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in ) is __________.

If  , the value of line integral . dr evaluated over contour C formed by the segments  is ______________.

If then div(uA) at (1, 1, 1) is ____________.

The open loop transfer function of a unity feedback system is given by

In G(s) plane, the Nyquist plot of G(s) passes through the negative real axis at the point

The current I flowing in the circuit shown below in amperes (round off to one decimal place) is ____________.

The asymptotic Bode magnitude plot of a minimum phase transfer function G(s) is shown below.

Consider the following two statements.

Statement I: Transfer function G(s) has three poles and one zero.

Statement II: At very high frequency , the phase angle         

Which one of the following options is correct?

The output response of a system is denoted as y(t), and its Laplace transform is given by   the steady state value of y(t)  is

The current I flowing in the circuit shown below in amperes is ________.

The rank of the matrix,  is __________________.

A co-axial cylindrical capacitor shown in figure (i) has dielectric with relative permittivity. When one-fourth portion of the dielectric is replaced with another dielectric of relative permittivity, as shown in Figure (ii), the capacitance is doubled. The value of  is ___

M is a 2 × 2 matrix with eigenvalues 4 and 9. The eigenvalues of  are

Consider a matrix , where, and  are the column vectors. Suppose , where  and  are the row vectors. Consider the following statements:

Statement 1:

Statement 2:

Five alternators each rated 5 MVA. 13.2 kV with 25% of reactance on its own base are connected in parallel to a busbar. The short-circuit level in MVA at the busbar is _____________.

A 30 kV, 50 Hz, 50 MVA generator has the positive, negative, and zero sequence reactances of 0.25 pu, 0.15 pu, and 0.05 pu, respectively. The neutral of the generator is grounded with a reactance so that the fault current for a bolted LG fault and that of a bolted three-phase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to two decimal place) is ________.

A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, 50 Hz AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmonic component in the AC input current is

In the circuit below, the operational amplifier is ideal. If  and , the output voltage () is        

A single-phase fully-controlled thyristor converter is used to obtain an average voltage of 180 V with 10 A constant current to feed a DC load. It is fed from single-phase AC supply of 230 V, 50 Hz. Neglect the source impedance. The power factor (round off to two decimal places) of AC mains is ________.

A fully-controlled three-phase bridge converter is working from a 415 V, 50 Hz AC supply. It is supplying constant current of 100 A at 400 V to a DC load. Assume larger inductive smoothing and neglect overlap. The rms value of the AC line current in amperes (round off to two decimal places) is _________.        

A Three-phase synchronous motor draws 200 A from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at a power factor of 0.5 leading is.

The voltage across and the current through a load are expressed as follows        

The average power in watts (round off to one decimal place) consumed by the load is _______.

A 220 V (line), three-phase, Y-connected, synchronous motor has a synchronous impedance of .

The motor draws the rated current of 10 A at 0.8 pf leading. The rms value of line-to-line internal voltage in volts (round off to two decimal places) is _________.

A 220 V DC shunt motor takes 3 A at no-load. It draws 25 A when running at full-load at 1500 rpm. The armature and shunt resistances are  and  respectively. The no-load speed in rpm (round off to two decimal places) is _________.

A moving coil instrument having a resistance of , gives a full-scale deflection when the current is 10 mA. What should be the value of the series resistance, so that it can be used as a voltmeter for measuring potential difference up to 100 V?

The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is

A delta connected 3.7kW, 400V (line), three phase, 4-pole, 50-Hz squirrel-cage induction motor has following equivalent circuit parameters per phase referred to the stator:

,,

Neglect shunt branch in the equivalent circuit. The starting line current in amperes (round off to two decimal places) when it is connected to 100V (line), 10Hz, three-phase AC source is ___________.

A 5 kVA, 50 V/100 V, single-phase transformer has a secondary terminal voltage of 95 V when loaded. The regulation of the transformer is.

A single-phase transformer of rating 25 kVA, supplies a 12 kW load at power factor of 0.6 lagging. The additional load at unity power factor in kW (round off to two decimal places) that may be added before this transformer exceeds its rated kVA is __________.

The magnetic circuit shown below has uniform cross-sectional area and air gap of 0.2 cm. The mean path length of the core is 40 cm. Assume that leakage and fringing fluxes are negligible. When the core relative permeability is assumed to be infinite, the magnetic flux density computed in the air gap is 1 tesla. With same Ampere-turns, if the core relative permeability is assumed to be 1000 (linear), the flux density in tesla (round off to three decimal places) calculated in the air gap is ____________.

A three-phase 50Hz, 400kV transmission line is 300 km long. The line inductance is 1mH/phase and capacitance 0.01µF/km per phase. The line is under open circuit condition at receiving end and energized with 400kV at sending end, the receiving end line voltage is KV (round off to two decimal places) will be ______

In the single machine infinite bus system shown below, the generator is delivering the real power of 0.8 pu at 0.8 power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is _________.