Let   and  be two signals whose Fourier Transforms are as shown in the figure shown below, In the figure,  denotes the impulse response.

For the system shown above, the minimum sampling rate required to sample y(t), so that y(t) can be uniquely reconstructed from its samples, is

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

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

Consider the function  where z is a complex variable and  denotes it complex conjugate. Which one of the following is TRUE?

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

The solution of the differential equation, for ,  with initial conditions y(0) = 0 and , is (u(t) denotes the unit step function),

The Boolean expression  simplifies to

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

Let y(x) be the solution of the differential equation  with initial conditions y(0) = 0 and . Then the value of y(1) is_______________.

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

Suppose the maximum frequency in a band-limited signal x(t) is 5kHz. Then, the maximum frequency in x(t)cos, in kHz, is ____________.

The value of the integral  is equal to          

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

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

Let the probability density function of a random variable, X, be given as:

where u(x) is the unit step function.

Then the value of ‘a’ and , respectively, are

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

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

The closed loop system will be stable if.

The output expression for the Karnaugh map shown below is

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

A three-phase voltage source inverter (VSI) as shown in the figure is feeding a delta connected resistive load of /phase. If it is fed from a 600V battery, with  conduction of solid-state devices, the power consumed by the load, in kW, is_____________.

The single line diagram of a balanced power system is shown in the figure, The voltage magnitude at the generator internal bus is constant 1.0pu magnitude. The p.u. reactance’s of different components in the system are also shown in  the figure. The infinite bus voltage magnitude is 1.0p.u. A three phase fault occurs at the middle of line 2. The ratio of the maximum real power that can be transferred during the pre-fault condition to the maximum real power that can be transferred under the faulted condition is_______________.

The flux linkage  and current (i) relation for an electromagnetic system is . When  I = 2A and g (air-gap length) = 10 cm, the magnitude of mechanical force on the moving part, in N, 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 the figure below. Conductor is parallel to and at 1 m distance from the z-axis. The speed of the conductor in r.p.m. required to induce a voltage of 1V across it, should be ___________.

In the circuit shown below, the initial capacitor voltage is 4V, Switch \(S_1\) is closed at t = 0. The charge (in ) lost by the capacitor from t = 25 micro sec.   to   is ______________.

The value of the line integral  along a path joining the origin (0, 0, 0) and the point (1, 1, 1) is

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

A power system with two generators is shown in the figure below. The system (generators, buses and transmission lines) is protected by six over current relays  to . Assuming a mix of directional and non directional relays at appropriate locations, the remote backup relays for  are

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

A buck-boost DC-DC converter, shown in the figure below, is used to convert 24V battery voltage to 36 V DC voltage to feed a load of 72W. It is operated at 20kHz with an inductor of 2mH and output capacitor 1000μF. All devices are considered to be ideal. The peak voltage across the solid-state switch (S), in volt, is____________.

A DC-DC boost converter, as shown in the figure below, is used to boost 360V to 400V, at a power of a 4kW. All devices are ideal, considering continuous inductor current, the rms current in the solid state switch (S), in ampere, is_______________.

A second-order real system has the following properties: 

(a) the damping ratio  and undamped natural frequency ,

(b) the steady state value of the output, to a unit step input, is 1.02

The transfer function of the system is

A parallel plate capacitor filled with two dielectric 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

In the circuit shown below, the voltage and current sources are ideal. The voltage   across the current source, in volts, is  

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

Consider a linear time-invariant system with transfer function                

If the input is cos(t) and the steady output is  , then the value of A is___________.

A  matrix P is such that, . Then the eigenvalues of P are

Let . Consider the set S of all vectors  such that  where . Then S is

A 50MVA, 10kV, 50Hz, 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 generator terminals, the ratio of initial and final values of the sinusoidal component of the short circuit current is______________.

Two identical unloaded generators are connected in parallel as shown in the figure. Both the generators are having positive, negative and zero sequence impedance of j0.4 p.u., j0.3 p.u. and j0.15 p.u. respectively. If the pre-fault voltage is 1 p.u. for a line-to-ground (L-G) fault at the terminals at the generators, the fault current, in p.u. is______________.

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

A full-bridge converter supplying an RLE load is shown in figure. The firing angle of the bridge converter is  . The supply voltage . . The inductor L is large enough to make the output current  a smooth dc current. Switches are lossless. The real power fed back to the source, in kW, is____________.

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 400V with power of 5kW from a source  V (rms), 50Hz sinusoidal AC mains at unity p.f. If its AC side interfacing inductor is 5mH and the switches are operated at 20kHz, then the phase shift  between AC mains voltage  and fundamental AC rms VSC voltage , in degrees, is_____.

A resistance and a coil connected in series and supplied from a phase, 100V, 50Hz ac source as shown in the figure below. The rms values of possible voltages across the resistance  and coil  respectively, in volts are

`

The circuit shown below is an example of a

The voltage (V) and current ((A) across a load are as follows.

.

.

The average power consumed by the load, in W, is_____________.

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

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

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

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

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

Three-phase transformers are connected to form a delta-star three-phase transformer of . The transformer supplies at 11kV a load of 8 MW at 0.8 p.f. lagging to a nearby plant. Neglect the transformer losses. The ratio of phase current in delta to star side is

The inductance and capacitance of a 400kV, three-phase, 50 Hz lossless transmission line are 1.6 mH/km/phase and 10 mF/km/phase respectively. The sending end voltage is maintained at 400kV. To maintain a voltage of 400kV at the receiving end, when the line is delivering 300MW load, the shunt compensation required is

At no load condition, a 3-phase, 50Hz, losses power transmission line has sending-end and receiving-end voltages of 400kV and 420kV respectively. Assuming the velocity of travelling wave to be the velocity of light, the length of the line, in km, is______________.

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.f. of the motor is_______________.