Consider the inverting amplifier, using an ideal operational amplifier shown in figure. The designer wishes to realize the input resistance seen by the small signal source to be as large as possible, while keeping the voltage gain between $$–10$$ and $$–25.$$ the upper limit on $${R_F}$$ is $$1\,M\Omega .$$ The value of $${R_1}$$ should be

Assume that the threshold voltage of the $$N$$-channel $$MOSFET$$ shown in figure is $$0.75$$ $$V.$$ The output characteristics of the $$MOSFET$$ are also shown

The Transconductance of the $$MOSFET$$ is

Assume that the threshold voltage of the $$N$$-channel $$MOSFET$$ shown in figure is $$0.75$$ $$V.$$ The output characteristics of the $$MOSFET$$ are also shown

The voltage gain of the amplifier is

The common emitter amplifier shown in the figure is biased using a $$1mA$$ ideal current source. The approximate base current value is_____.

Assume that the $$N$$-channel $$MOSFET$$ shown in figure is ideal, and that its threshold voltage is The voltage $${\rm I}V,$$ the voltage $${{V_{ab}}}$$ between nodes $$'a'$$ and $$'b'$$ is

The typical frequency response of a two-stage direct coupled voltage amplifier is as shown in figure

In the given figure, if the input is a sinusoidal signal, the output-will appear as shown

Assume that $${D_1}$$ and $${D_2}$$ in figure are ideal diodes the value of current $${I_s}$$ is

In the $$GH(s)$$ plane, the Nyquist plot of the loop transfer function $$G\left( s \right)\,H\left( s \right) = {{\pi {e^{ - 0.25s}}} \over s}$$ passes through the negative real axis at the point

A state variable system
$$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \right)u\left( t \right)$$ with the initial condition $$X\left( 0 \right) = {\left[ { - 1\,\,3} \right]^T}$$ and the unit step input $$u(t)$$ has

The state transition equation

A state variable system
$$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \right)u\left( t \right)$$ with the initial condition $$X\left( 0 \right) = {\left[ { - 1\,\,3} \right]^T}$$ and the unit step input $$u(t)$$ has

The state transition matrix

If the compensated system shown in the figure has a phase margin of $${60^ \circ }$$ at the crossover frequency of $$1 rad/sec,$$ the value of the gain $$K$$ is

A system with zero initial conditions has the closed loop transfer function $$T\left( s \right) = {{{s^2} + 4} \over {\left( {s + 1} \right)\left( {s + 4} \right)}}.$$ The system output is zero at the frequency

The gain margin of a unity feedback control system with the open loop transfer function $$G\left( s \right) = {{\left( {s + 1} \right)} \over {{s^2}}}$$ is

When subjected to a unit step input, the closed loop control system shown in the figure will have a steady state error of

Figure shows the root locus plot (location of poles not given) of a third order system whose open loop transfer function is

When subjected to a unit step input, the closed loop control system shown in the figure will have a steady state error of

The $$8085$$ assembly language instruction that stores the content of $$H$$ and $$L$$ registers into the memory locations $$2050H$$ and $$2051H,$$ respectively, is

If $${X_1}$$ and $${X_2}$$ are the inputs to the circuit shown in the figure, the output $$Q$$ is

A digital-to-analog converter with a full -scale output voltage of $$3.5$$ $$V$$ has a resolution close to $$14$$ $$m$$ $$V.$$ Its bit size is

Select the circuit which will produce the given output $$Q$$ for the input signals $${X_1}$$ and $${X_2}$$ given in the figure.

The digital circuit shown in the figure works as a

In the figure, as long as $${X_1} = 1$$ and $${X_2} = 1,$$ the output $$Q$$ remains

In the figure given below the value of $$R$$ is

Two networks are connected in cascade as shown in the Fig. With the usual notations the equivalent $$A,B,C$$ and $$D$$ constants are obtained. Given that, $$C$$ $$ = 0.025\angle {45^ \circ },$$ the value of $${Z_2}$$ is

For the two port network shown in the Fig. the $$Z$$ $$-$$ matrix is given by

The $$RL$$ circuit of the figure is fed from a constant magnitude, variable frequency sinusoidal voltage source $${V_{IN.}}$$ At $$100Hz,$$ the $$R$$ and $$L$$ elements each have a voltage drop $${u_{RMS}}.$$ If the frequency of the source is changed to $$50Hz,$$ then new voltage drop across $$R$$ is

The circuit shown in the Fig. is in steady state, when the switch is closed at $$t=0.$$ Assuming that the inductance is ideal, the current through the inductor at $$t = {0^ + }$$ equals

A coil of inductance $$10$$ $$H$$ resistance $$40\,\,\Omega $$ is connected as shown in Fig. After the switch $$S$$ has been in connection with point $$1$$ for a very long time, it is moved to point $$2$$ at $$t = 0.$$

If, at $$t = {0^ + }$$, the voltage across the coil is $$120$$ $$V,$$ the value of resistance $$R$$ is

A coil of inductance $$10$$ $$H$$ resistance $$40\,\,\Omega $$ is connected as shown in Fig. After the switch $$S$$ has been in connection with point $$1$$ for a very long time, it is moved to point $$2$$ at $$t = 0.$$

For the value of $$R$$ obtained in the above question, the time taken for $$95\% $$ of the stored energy to be dissipated is close to

In the Fig. given below, the initial capacitor voltage is zero. The switch is closed at $$t = 0.$$ the final steady-state voltage across the capacitor is

In the given Fig. the Thevenin's equivalent pair (voltage, impedence), as seen at the terminals $$P-Q$$, is given by

A digital-to-analog converter with a full scale output voltage of $$3.5V$$ has resolution close to $$14mV.$$ It's bit size is _____.

The simultaneous application of signals $$x(t)$$ and $$y(t)$$ to the horizontal and vertical plates, respectively, of an oscilloscope, produces a vertical figure-of-$$8$$ display. If $$P$$ and $$Q$$ are constants, and $$x(t)=P$$ $$sin(4t+30),$$ then $$y(t)$$ is equal to

A $$PMMC$$ voltmeter is connected across a series combination of a $$DC$$ voltage source $${V_1} = 2V$$ and $$AC$$ voltage source $${V_2}\left( t \right) = 3$$ $$sin(4t)$$ $$V.$$ The meter reads

Two wattmeter's, which are connected to measure the total power on a three-phase system supplying a balanced load, read $$10.5$$ $$kW$$ and $$–2.5$$ $$kW$$ respectively. The total power and the power factor respectively are

A DC ammeter has a resistance of $$0.1$$$$\Omega $$ and its current range is $$0$$ – $$100A.$$ If the range is to be extended to $$0$$ –$$500A,$$ the meter requires the following shunt resistance

A $$1000$$ $$V$$ $$DC$$ supply has two $$1-core$$ cables as its positive and negative leads: their insulation resistances to earth are $$4\,\,M\Omega $$ and $$6\,\,M\Omega $$, respectively, as shown in figure. A voltmeter with resistance $$50\,\,k\Omega $$ is used to measure the insulation of the cable. When connected between the positive core and earth, the voltmeter reads

The set-up in the figure is used to measure resistance $$R$$. The ammeter and voltmeter resistances are $$0.01$$$$\Omega $$ and $$2000$$$$\Omega $$, respectively. Their readings are $$2A$$ and $$180$$ $$V$$, respectively, giving a measured resistance of $$90$$ $$\Omega $$. The percentage error in the measurement is

A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous reactance of $$20\Omega .$$ Neglect the armature resistance and consider operation at full load and unity power factor.

The power angle is close to

A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous reactance of $$20\Omega .$$ Neglect the armature resistance and consider operation at full load and unity power factor.

The induced $$emf$$ is close to (line to line)

For an induction motor, operating at a slip 's', the ratio of gross power output to air gap power is equal to:

In relation to the synchronous machines, which one of the following statements is false?

In a single phase induction motor driving a fan load, the reason for having a high resistance rotor is to achieve

Assertion [a]: Under V/f control of induction motor, the maximum value of the developed torque remains constant over a wide range of speed in the subsynchronous region.

Reason [r]: The magnetic flux is maintained almost constant at the rated value by keeping the ratio V/f constant over the considered speed range.

A three-phase cage induction motor is started by direct-on-line (DOL) switching at the rated voltage. If the starting current drawn is 6 times the full load current, and the full load slip is 4%, the ratio of the starting developed torque to the full load torque is approximately equal to

Under no load condition, if the applied voltage to an induction motor is reduced from the rated voltage to half the rated value,

On the torque/speed curve of induction motor shown in Fig, four points of operation are market as W, X, Y and Z. Which one of them represents the operation at a slip greater than 1?

Which three-phase connection can be used in a transformer to introduce a phase difference of 30° between its output and corresponding input line voltages

In relation to DC machines, match the following and choose the correct combination.

Group-I(Performance variables)
(P) Armature emf (E)
(Q) Developed torque (T)
(R) Developed power (P)

Group-II(Proportional to)
1.Flux ($$\phi$$), speed ($$\omega$$) and armature current ($$I_a$$)
2.$$\phi$$ and $$\omega$$ only
3.$$\phi$$ and $$I_a$$ only
4.$$I_a$$ and $$\omega$$ only
5.$$I_a$$ only

A 50 kW dc shunt motor is loaded to draw rated armature current at any given speed. When driven
(i) at half the rated speed by armature voltage control and
(ii) at 1.5 times the rated speed by field control, the respective output powers delivered by the motor are approximately

Two magnetic poles revolve around a stationary armature carrying two coils ($$c_1-c'_1$$ , $$c_2-c'_2$$ ) as shown in Figure. Consider the instant when the poles are in a position as shown. Identify the correct statement regarding the polarity of the induced emf at this instant in coil sides $$c_2$$ and $$c_1$$.

If $$S = \int\limits_1^\infty {{x^{ - 3}}dx} $$ then $$S$$ has the value

For the function $$f\left( x \right) = {x^2}{e^{ - x}},$$ the maximum occurs when $$x$$ is equal to

If $$R = \left[ {\matrix{ 1 & 0 & { - 1} \cr 2 & 1 & { - 1} \cr 2 & 3 & 2 \cr } } \right]$$ then the top row of $${R^{ - 1}}$$ is

For the matrix $$P = \left[ {\matrix{ 3 & { - 2} & 2 \cr 0 & { - 2} & 1 \cr 0 & 0 & 1 \cr } } \right],$$ one of the eigen values is $$-2.$$ Which of the following is an eigen vector?

In the matrix equation $$PX=Q$$ which of the following is a necessary condition for the existence of atleast one solution for the unknown vector $$X.$$

for the scalar field $$u = {{{x^2}} \over 2} + {{{y^2}} \over 3},\,\,$$ the magnitude of the gradient at the point $$(1,3)$$ is

For the equation $$\,\,\mathop x\limits^{ \bullet \bullet } \left( t \right) + 3\mathop x\limits^ \bullet \left( t \right) + 2x\left( t \right) = 5,\,\,\,$$ the solution $$x(t)$$ approaches the following values as $$t \to \infty $$

The solution of the first order differential equation $$\mathop x\limits^ \bullet \left( t \right) = - 3\,x\left( t \right),\,x\left( 0 \right) = {x_0}\,\,\,\,$$ is

A fair coin is tossed $$3$$ times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is

If $$P$$ and $$Q$$ are two random events, then which of the following is true?

The output voltage waveform of a three - phase square-wave inverter contains

The given figure shows a step $$-$$ down chopper switched at $$1$$ $$KHz$$ with a duty ratio $$D = 0.5.$$ The peak - peak ripple in the load current is close to

Consider a phase $$-$$ controlled converter shown in figure The thyristor is fired at an angle $$\alpha $$ in every positive half cycle of the input voltage. If the peak value of the instantaneous output voltage equals $$230$$ $$V,$$ the firing angle $$\alpha $$ is close to

A three - phase diode bridge rectifier is fed from a $$400$$ $$V$$ $$RMS$$. $$50$$ $$Hz$$, three $$-$$ phase $$AC$$ source. If the load is purely resistive, then peak instantaneous output voltage is equal to

An electronic switch $$S$$ is required to block voltages of either polarity during its OFF state as shown in figure (a). This switch is required to conduct in only one direction during its ON state as shown in the figure (b).

Which of the following are valid realizations of the switch $$s$$?

The figure shows the voltage across a power semiconductor device and the current through the device during a switching transition. Is the transition a turn ON transition or a turn OFF transition? What is the energy lost during the transition?

The conduction loss versus device current characteristic of a power $$MOSFET$$ is best approximated by

At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-line to ground fault level is $$5000$$ MVA. Neglecting the resistance and the shunt susceptances of the system.

The positive sequence driving point reactance at the bus is

The p.u. parameters for a $$500$$ MVA machine on its own base are:
Inertia, M = $$20$$ p.u.; reactance X = $$2$$ p.u. The p.u. values of inertia and reactance on $$100$$ MVA common base, respectively are

High Voltage DC (HVDC) transmission is mainly used for

The network shown in the given figure has impedances in p.u. as indicated. The diagonal element $$Y22$$ of the bus admittance matrix $${Y_{BUS}}$$ of the network is

At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-line to ground fault level is $$5000$$ MVA. Neglecting the resistance and the shunt susceptances of the system.

The zero sequence driving point reactance at the bus is

The parameters of transposed overhead transmission line are given as: self reactance $${X_s} = 0.4\,\,\Omega /km$$ and Mutual reactance $$\,{X_m} = 0.1\,\,\Omega /km.\,\,$$ The positive sequence reactance $${X_1}$$ and zero sequence reactance $${X_0}$$ respectively in $$\Omega /km$$ are

A generator with constant 1.0 p.u. terminal voltage supplies power through a step-up transformer of 0.12 p.u. reactance and a double-circuit line to an infinite bus bar as shown in the figure. The infinite bus voltage is maintained at 1.0 p.u. Neglecting the resistances and susceptances of the system, the steady state stability power limit of the system is 6.25 p.u. If one of the double-circuit is tripped, the resulting steady state stability power limit in p.u. will be

A load centre is at an equidistant from the two thermal generating stations $${G_1}$$ and $${G_2}$$ as shown in figure. The fuel cost characteristics of the generating stations are given by
$${F_1} = a + b{P_1} + cP_1^2\,Rs/hour$$
$${F_2} = a + b{P_2} + 2cP_2^2\,Rs/hour$$

Where $${P_1}$$ and $${P_2}$$ are the generations in $$MW$$ of $${G_1}$$and $${G_2}$$, respectively. For most economic generation to meet $$300MW$$ of load $${P_1}$$ and $${P_2},$$ respectively, are

At an industrial sub-station with a $$4$$ $$MW$$ load, a capacitor of $$2$$ MVAR is installed to maintain the load power factor at $$0.97$$ lagging. If the capacitor goes out of service, the load power factor becomes

The insulation strength of an EHV transmission line is mainly governed by

For the triangular waveform shown in the figure, the $$RMS$$ value of the voltage is equal to

If u(k) is the unit step and $$\delta\left(k\right)$$ is the unit impulse function, the inverse z-transform of $$F\left(z\right)=\frac1{z+1}$$ for k>0 is:

For the equation $$\ddot x\left(t\right)+3\dot x\left(t\right)+2x\left(t\right)=5$$, the solution x(t) approaches which of the following values as t$$\rightarrow\infty$$ ?

The Laplace transform of a function f(t) is F(s) = $$\frac{5s^2+23s+6}{s\left(s^2+2s+2\right)}$$. As $$t\rightarrow\infty$$, f(t) approaches

The Fourier series for the function f(x) = sin² x is

The RMS value of the voltage v(t) = 3 + 4cos(3t) is