GATE EE 2016 PYQ

For the circuit shown below, taking the opamp as ideal, the output voltage in terms of the input voltages is

A transistor circuit is given below. The Zener diode breakdown voltage is 5.3 V as shown. Take base to emitter voltage drop to be 0.6 V. The value of the current gain is _________.

The circuit shown below is an example of a

Loop transfer function of a feedback system is . Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of G(s)H(s) encircles -1+ j0

A second-order real system has the following properties: a) the damping ratio = 0.5 and undamped natural frequency =10 rad/s, b) the steady state value of the output, to a unit step input, is 1.02. Th

The open loop transfer function of a unity feedback control system is given by The closed loop system will be stable if,

For the network shown in the figure below, the frequency (in rad/s) at which the maximum phase lag occurs is, ___________.

Consider a linear time invariant system , with initial condition at t=0. Suppose are eigenvectors of (2 x 2) matrix A corresponding to distinct eigenvalues respectively. Then the response of the syste

The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function is

The phase cross-over frequency of the transfer function in rad/s is

Given the following polynomial equation , the number of roots of the polynomial, which have real parts strictly less than -1, is ________ .

Consider the following asymptotic Bode magnitude plot ( is in rad/s). Which one of the following transfer functions is best represented by the above Bode magnitude plot?

The Boolean expression simplifies to

The current state of a two JK flip-flop system is 00. Assume that the clock rise-time is much smaller than the delay of the JK flip-flop. The next state of the system is

A 2-bit flash Analog to Digital Converter (ADC) is given below. The input is Volts. The expression for the LSB of the output as a Boolean function of is

A temperature in the range of -40 C to 55 C is to be measured with a resolution of 0.1 C. The minimum number of ADC bits required to get a matching dynamic range of the temperature sensor is

Consider the following circuit which uses a 2-to-1 multiplexer as shown in the figure below. The Boolean expression for output F in terms of A and B is

The circuit below is excited by a sinusoidal source. The value of R, in , for which the admittance of the circuit becomes a pure conductance at all frequencies is _____________.

A resistance and a coil are connected in series and supplied from a single phase, 100 V, 50 Hz ac source as shown in the figure below. The rms values of plausible voltages across the resistance ( ) an

The z-parameters of the two port network shown in the figure are and . The average power delivered to , in watts, is _______.

In the circuit shown, switch has been closed for a long time. At time t=0 switch is closed. At , the rate of change of current through the inductor, in amperes per second, is _____.

The following figure shows the connection of an ideal transformer with primary to secondary turns ratio of 1:100. The applied primary voltage is 100 V (rms), 50 Hz, AC. The rms value of the current I,

The driving point input impedance seen from the source of the circuit shown below, in , is ______.

The graph associated with an electrical network has 7 branches and 5 nodes. The number of independent KCL equations and the number of independent KVL equations, respectively, are

In the balanced 3-phase, 50 Hz, circuit shown below, the value of inductance (L) is 10 mH. The value of the capacitance (C) for which all the line currents are zero, in millifarads, is ___________.

In the circuit shown below, the initial capacitor voltage is 4 V. Switch is closed at t=0. The charge (in C) lost by the capacitor from t=25 to t=100 is ____________.

The voltage (V) and current (A) across a load are as follows. , . The average power consumed by the load, in W, is___________.

In the circuit shown below, the supply voltage is volts. The peak value of the steady state current through the 1 resistor, in amperes, is ______.

An energy meter, having meter constant of 1200 revolutions/kWh, makes 20 revolutions in 30 seconds for a constant load. The load, in kW, is _____________.

A dc voltage with ripple is given by volts. Measurements of this voltage , made by moving-coil and moving-iron voltmeters, show readings of respectively. The value of , in volts, is _________.

A single-phase, 2 kVA, 100/200 V transformer is reconnected as an auto-transformer such that its kVA rating is maximum. The new rating, in kVA, is ______.

The starting line current of a 415 V, 3-phase, delta connected induction motor is 120 A, when the rated voltage is applied to its stator winding. The starting line current at a reduced voltage of 110

Consider a system consisting of a synchronous generator working at a lagging power factor, a synchronous motor working at an overexcited condition and a directly grid-connected induction generator. Co

Three single-phase transformers are connected to form a delta-star three-phase transformer of 110 kV/ 11 kV. The transformer supplies at 11 kV a load of 8 MW at 0.8 p.f. lagging to a nearby plant. Neg

The flux linkage ( ) and current (i) relation for an electromagnetic system is . When i=2A and g (air-gap length)=10cm, the magnitude of mechanical force on the moving part, in N, is ________.

The direction of rotation of a single-phase capacitor run induction motor is reversed by

A three-phase, 50 Hz salient-pole synchronous motor has a per-phase direct-axis reactance ( ) of 0.8 pu and a per-phase quadrature-axis reactance ( ) of 0.6 pu. Resistance of the machine is negligible

If an ideal transformer has an inductive load element at port 2 as shown in the figure below, the equivalent inductance at port 1 is

A single-phase 400 V, 50 Hz transformer has an iron loss of 5000 W at the rated condition. When operated at 200 V, 25 Hz, the iron loss is 2000 W. When operated at 416 V, 52 Hz, the value of the hyste

In a constant V/f induction motor drive, the slip at the maximum torque

A DC shunt generator delivers 45 A at a terminal voltage of 220 V. The armature and the shunt field resistances are 0.01 and 44 respectively. The stray losses are 375 W. The percentage efficiency of t

A single-phase, 22 kVA, 2200 V/ 220 V, 50 Hz, distribution transformer is to be connected as an auto-transformer to get an output voltage of 2420 V. Its maximum kVA rating as an autotransformer is

A 4-pole, lap-connected, separately excited dc motor is drawing a steady current of 40 A while running at 600 rpm. A good approximation for the waveshape of the current in an armature conductor of the

The power consumption of an industry is 500 kVA, at 0.8 p.f. lagging. A synchronous motor is added to raise the power factor of the industry to unity. If the power intake of the motor is 100 kW, the p

In cylindrical coordinate system, the potential produced by a uniform ring charge is given by , where f is a continuous function of r and z. Let be the resulting electric field. Then the magnitude of

A soft-iron toroid is concentric with a long straight conductor carrying a direct current I. If the relative permeability of soft-iron is 100, the ratio of the magnetic flux densities at two adjacent

Two electric charges q and -2q are placed at (0,0) and (6,0) on the x-y plane. The equation of the zero equipotential curve in the x-y plane is

Two electrodes, whose cross-sectional view is shown in the figure below, are at the same potential. The maximum electric field will be at the point

A parallel plate capacitor filled with two dielectrics is shown in the figure below. If the electric field in the region A is 4 kV/cm, the electric field in the region B, in kV/cm, is

A rotating conductor of 1 m length is placed in a radially outward (about the z-axis) magnetic flux density (B) of 1 Tesla as shown in figure below. Conductor is parallel to and at 1 m distance from t

The line integral of the vector field along a path from (0,0,0) to (1,1,1) parametrized by (t, , t) is _____.

A buck-boost DC-DC converter, shown in the figure below, is used to convert 24 V battery voltage to 36 V DC voltage to feed a load of 72 W. It is operated at 20 kHz with an inductor of 2 mH and output

The voltage ( ) across and the current ( ) through a semiconductor switch during a turn-ON transition are shown in figure. The energy dissipated during the turn-ON transition, in mJ, is _______.

The switches T1 and T2 in Figure (a) are switched in a complementary fashion with sinusoidal pulse width modulation technique. The modulating voltage and the triangular carrier voltage ( ) are as show

A full-bridge converter supplying an RLE load is shown in figure. The firing angle of the bridge converter is 120 . The supply voltage , , E=800 V. The inductor L is large enough to make the output cu

A buck converter, as shown in Figure (a) below, is working in steady state. The output voltage and the inductor current can be assumed to be ripple free. Figure (b) shows the inductor voltage during a

A steady dc current of 100 A is flowing through a power module (S,D) as shown in Figure (a). The V-I characteristics of the IGBT (S) and the diode (D) are shown in Figures (b) and (c), respectively. T

A three-phase Voltage Source Inverter (VSI) as shown in the figure is feeding a delta connected resistive load of 30 /phase. If it is fed from a 600 V battery, with 180 conduction of solid-state devic

A single-phase full-bridge voltage source inverter (VSI) is fed from a 300 V battery. A pulse of 120 duration is used to trigger the appropriate devices in each half-cycle. The rms value of the fundam

A single-phase bi-directional voltage source converter (VSC) is shown in the figure below. All devices are ideal. It is used to charge a battery at 400 V with power of 5 kW from a source =220 V (rms),

A three-phase diode bridge rectifier is feeding a constant DC current of 100 A to a highly inductive load. If three-phase, 415 V, 50 Hz AC source is supplying to this bridge rectifier then the rms val

A single-phase thyristor-bridge rectifier is fed from a 230 V, 50 Hz, single-phase AC mains. If it is delivering a constant DC current of 10 A, at firing angle of 30 , then value of the power factor a

A DC-DC boost converter, as shown in the figure below, is used to boost 360V to 400 V, at a power of 4 kW. All devices are ideal. Considering continuous inductor current, the rms current in the solid

If the star side of the star-delta transformer shown in the figure is excited by a negative sequence voltage, then

The magnitude of three-phase fault currents at buses A and B of a power system are 10 pu and 8 pu, respectively. Neglect all resistances in the system and consider the pre-fault system to be unloaded.

A 50 MVA, 10 kV, 50 Hz, star-connected, unloaded three-phase alternator has a synchronous reactance of 1 p.u. and a sub-transient reactance of 0.2 p.u. If a 3-phase short circuit occurs close to the g

Two identical unloaded generators are connected in parallel as shown in the figure. Both the generators are having positive, negative and zero sequence impedances of j0.4 p.u., j0.3 p.u. and j0.15 p.u

A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipatio

In a 100 bus power system, there are 10 generators. In a particular iteration of Newton Raphson load flow technique (in polar coordinates), two of the PV buses are converted to PQ type. In this iterat

A 30 MVA, 3-phase, 50 Hz, 13.8 kV, star-connected synchronous generator has positive, negative and zero sequence reactances, 15%, 15% and 5% respectively. A reactance ( ) is connected between the neut

At no load condition, a 3-phase, 50 Hz, lossless power transmission line has sending-end and receiving-end voltages of 400 kV and 420 kV respectively. Assuming the velocity of traveling wave to be the

A power system with two generators is shown in the figure below. The system (generators, buses and transmission lines) is protected by six overcurrent relays . Assuming a mix of directional and nondir

A power system has 100 buses including 10 generator buses. For the load flow analysis using Newton-Raphson method in polar coordinates, the size of the Jacobian is

The inductance and capacitance of a 400 kV, three-phase, 50 Hz lossless transmission line are 1.6 mH/km/phase and 10 nF/km/phase respectively. The sending end voltage is maintained at 400 kV. To maint

A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1 m in a horizontal plane. This is now converted to a three-phase transmissi

The single line diagram of a balanced power system is shown in the figure. The voltage magnitude at the generator internal bus is constant and 1.0 p.u. The p.u. reactances of different components in t

Consider a causal LTI system characterized by differential equation . The response of the system to the input . where u(t) denotes the unit step function, is

Suppose have the Fourier transforms as shown below. Which one of the following statements is TRUE?

The Laplace Transform of is

Let be two signals whose Fourier Transforms are as shown in the figure below. In the figure, denotes the impulse response. For the system shown above, the minimum sampling rate required to sample y(t)

The transfer function of a system is . The steady state output y(t) is for the input cos(2t). The values of A and , respectively are

The value of is the Dirac delta function, is

Let . The value of in the range , such that is _______.

Consider a linear time-invariant system with transfer function If the input is cos(t) and the steady state output is , then the value of A is _________.

Suppose the maximum frequency in a band-limited signal is 5 kHz. Then, the maximum frequency in , in kHz, is ________.

Consider a continuous-time system with input x(t) and output y(t) given by y(t) = x(t) cos(t) This system is

Let f(x) be a real, periodic function satisfying f(-x)=-f(x). The general form of its Fourier series representation would be

The output of a continuous-time, linear time-invariant system is denoted by T{x(t)} where x(t) is the input signal. A signal z(t) is called eigen-signal of the system T, when , where is a complex numb

Consider the following state-space representation of a linear time-invariant system. and The value of y(t) for is______.

The value of the integral is equal to