An op-amp, having a slew rate of $$62.8$$ $$V/\mu \,$$sec, is connected in a voltage follower configuration. If the maximum amplitude of the input sinusoidal is $$10$$ Volts. Then the minimum frequency at which the slew rate limited distortion would set in at the output is

For the oscillator circuit shown in figure, the expression for the time period of oscillations can be given by (where $$\tau = RC$$ )

For the op-amp circuit shown in figure. Determine the output voltage $${v_0}.$$ Assume that the op-amps are ideal

A simple active filter is shown in figure. Assume ideal op-amp. Derive the transfer function $${v_0}/{v_i}$$ of the circuit, and state the type of the filter (i.e., high-pass, low-pass, band-pass, or band-reject). Determine the required values of $${R_1},{R_2}$$ and $$C$$ in order for the filter to have a $$3$$-$$dB$$ frequency of $$1$$ $$kHz,$$ a high frequency input resistance of $$100\,\,k\Omega $$ and a high frequency gain magnitude of $$10.$$

An op-amp has an open-loop gain of $${10^5}$$ and an open-loop upper cutoff frequency of $$10$$ $$Hz.$$ If this op-amp is connected as an amplifier with a closed-loop gain of $$100,$$ then the new upper cutoff frequency is

In the single stage transistor amplifier circuit shown in figure, the capacitor $${C_E}$$ is removed. Then the ac small signal midband voltage gain of the amplifier

A sample-and-hold $$(S/H)$$ circuit, having a holding capacitor of $$0.1$$ $$nF,$$ is used at the input of an $$ADC$$ (analog-to-digital converter). The conversion time of the $$ADC$$ is $$1\,\,\mu \sec ,$$ and during this time, the capacitor should not lose more than $$0.5\% $$ of the charge put across it during the sampling time. The maximum value of the input signal to the $$S/H$$ circuit is $$5V.$$ The leakage current of the $$S/H$$ circuit should be less than

The transistor in the amplifier circuit shown in the figure is biased at $${{\rm I}_C} = mA.$$ Use $${V_T}\left( { = {{kT} \over q}} \right) = 26\,mV,$$ $${\beta _0} = 2000,\,{r_b} = 0$$ and $${r_0} \Rightarrow \infty $$
$$(a)$$ Determine the AC small signal midband voltage gain $$\left( {{\raise0.5ex\hbox{$\scriptstyle {{V_o}}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {{V_i}}$}}} \right)$$ of the circuit
$$(b)$$ Determine the required value of $${C_E}$$ for the circuit to have a lower cutoff frequency of $$10Hz$$

An $$N$$-channel $$JFET$$ having a pinch-off voltage $$\left( {{V_P}} \right)$$ of $$-5V$$ shows a transconductance (gm) of $$1$$ $$mA/V$$ when the applied Gate to source voltage $$\left( {{V_{GS}}} \right)$$ is $$-3V.$$ Its maximum transconductance (in $$mA/V$$) is

Given the characteristic equation $${s^3} + 2{s^2} + Ks + K = 0.$$ Sketch the root focus as $$K$$ varies from zero to infinity. Find the angle and real axis intercept of the asymptotes, break-away / break-in points, and imaginary axis crossing points, if any

The polar plot of a type-$$1, 3$$-pole, open-loop system is shown in Fig. below. The closed loop system is

The asymptotic approximation of the log-magnitude versus frequency plot of a minimum phase system with real poles and one zero is shown in Fig. Its transfer functions is

A unity feedback system has an open-loop transfer function of $$G\left( s \right) = {{10000} \over {s{{\left( {s + 10} \right)}^2}}}$$
(a) Determine the magnitude of $$G\left( {j\omega } \right)$$ in dB at an angular frequency of $$\omega = 20rad/\sec .$$
(b) Determine the phase margin in degrees.
(c) Determine the gain margin in $$dB.$$
(d) Is the system stable or unstable?

Given the homogeneous state-space equation $$\mathop X\limits^ \bullet = \left[ {\matrix{ { - 3} & 1 \cr 0 & { - 2} \cr } } \right]x$$ the steady state value of $$\,\,{x_{ss}}\,\, = \mathop {Lim}\limits_{t \to \infty } x\left( t \right),$$ given the initial state value of $$x\left( 0 \right) = {\left[ {10 - 10} \right]^T},\,\,is$$

The output of a logic gate is $$''1''$$ when all its inputs are at logic $$''0''.$$ The gate is either

The output $$f$$ of the $$4$$- to- $$1$$ $$MUX$$ shown in fig. is

For the ring counter shown in Fig. find the steady state sequence if the initial state of the counters is $$1110\,\,(i.e.,\,\,{Q_3},{Q_2},{Q_1},{Q_0} = 1110).$$ Determine the MOD number of the counter.

Among the following four, the slowest $$ADC$$ (analog-to-digital converter) is

An Intel $$8085$$ processor is executing the program given below.
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,MVIA,\,\,10H \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,MVIB,\,\,10H \cr & BACK:\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,NOP \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,ADD\,\,B \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,RLC \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,JNC\,\,BACK \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,HLT \cr} $$

The number of times that the operation $$NOP$$ will be executed is equal to

Two incandescent light bulbs of $$40$$ $$W$$ and $$60$$ $$W$$ rating are connected in series across the mains. Then

Given two coupled inductors $${L_1}$$ and $${L_2}$$, their mutual inductance $$M$$ satisfies

Consider the star network shown in Fig. The resistance between terminals $$A$$ and $$B$$ with $$C$$ open is $$6\,\Omega ,$$ between terminals $$B$$ and $$C$$ with $$A$$ open is $$11\,\Omega ,$$ and between terminals $$C$$ and $$A$$ with $$B$$ open is $$9\,\Omega $$ . The values of $${R_A},\,\,{R_B},\,\,{R_C}$$ are:

A unit step voltage is applied at $$t = 0$$ to a series $$RL$$ circuit with zero initial conditions.

In a series $$RLC$$ circuit at resonance, the magnitude of the voltage developed across the capacitor

Determine the resonance frequency and the $$Q$$ $$-$$ factor of the circuit shown in Fig.

Data: $$\,\,\,\,\,R = 10\,\Omega ,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C = 3\,\mu F,$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{L_1} = 40\,mH,\,\,\,\,\,\,\,\,{L_2} = 10\,mH$$
and $$\,\,\,\,\,\,\,\,M = 10\,mH.$$

A passive 2-port network is in a steady state.Compare to its input, the steady state output can never offer

Resistances $${R_1}$$ and $${R_2}$$ have, respectively, nominal values of $$10\Omega $$ and $$5\Omega ,$$ and tolerances of $$ \pm 5\% $$ and $$ \pm 10\% $$. The range of values for the parallel combination of $${R_1}$$ and $${R_2}$$ is

A $$100$$ $$\mu A$$ ammeter has an internal resistance of $$100\,\Omega $$. For extending its range to measure $$500$$ $$\mu A$$, the shunt required is of resistance (in $$\Omega $$)

The minimum number of wattmeter(s) required to measure 3 $$-$$ phase, 3 $$-$$ wire balanced or unbalanced power is

A $$50$$ $$kW$$ synchronous motor is tested by driving it by another motor. When the excitation is not switched on, the driving motor takes $$800$$ $$W.$$ When the armature is short-circuited and the rated armature current of $$10$$ $$A$$ is passed through it, the driving motor requires $$2500$$ $$W.$$ On open-circuiting the armature with rated excitation, the driving motor takes $$1800$$ $$W.$$ Calculate the efficiency of the synchronous motor at $$50\% $$ load. Neglect the losses in the driving motor.

Two identical synchronous generators, each of $$100$$ $$MVA,$$ are working in parallel supplying $$100$$ $$MVA$$ at $$0.8$$ lagging $$p.f.$$ at rated voltage. Initially the machines are sharing load equally. If the field current of first generator is reduced by $$5\% $$ and of the second generator increased by $$5\% ,$$ find the sharing of load ($$MW$$ and $$MVAR$$) between the generators.
Assume$${X_d} = {X_q} = 0.8\,\,p.u.$$ no field saturation and rated voltage across load. Reasonable approximations may be made.

In a $$dc$$ motor running at $$2000$$ $$rpm,$$ the hysteresis and eddy current losses are $$500$$ $$W$$ and $$200$$ $$W$$ respectively. If the flux remains constant, calculate the speed at which the total iron losses are halved.

A $$dc$$ series motor is rated $$230V,$$ $$1000$$ $$rpm,$$ $$80$$ $$A$$ (refer to Figure). The series field resistance is $$0.11\,\Omega ,$$ and the armature resistance is $$0.14\,\Omega .$$ If the flux at an armature current of $$20A$$ is $$0.4$$ times of that under rated condition, calculate the speed at this reduced armature current of $$20$$ $$A.$$

An ideal transformer has a linear $$B-H$$ characteristic with a finite slope and a turns ratio of $$1:1.$$ The primary of the transformer is energized with an ideal current source, producing the signal i as shown in figure. Sketch the shape (neglecting the scale factor) of the following signals, labeling the time axis clearly

$$(a)$$ $$\,\,\,\,\,$$ the core flux $${\phi _{oc}}$$ with the secondary of the transformer open
$$(b)$$ $$\,\,\,\,\,$$ the open-circuited secondary terminal voltage $${V_2}\left( t \right).$$
$$(c)$$ $$\,\,\,\,\,$$ the short-circuited secondary current $${i_2}\left( t \right)$$
$$(d)$$ $$\,\,\,\,\,$$ the core flux $${\phi _{sc}},$$ with the secondary of the transformer short-circuited.

In case of an armature controlled separately excited dc motor drive with closed loop speed control, an inner current loop is useful because it

An electric motor with 'constant output power' will have a torque speed characteristic in the form of a

A single-phase transformer is to be switched to the supply to have minimum inrush current. The switch should be closed at

The core flux of a practical transformer with a resistive load

A 3-phase transformer has rating of 20 MVA, 220 kV (star) / 33 kV (delta) with leakage reactance of 12%. The transformer reactance (in ohms) referred to each phase of the L.V. delta-connected side is

The hysteresis loop of a magnetic material has an area of 5 cm² with the scales given as 1 cm = 2 AT and 1 cm = 50 mWb. At 50 Hz, the total hysteresis loss is

It is desirable to eliminate 5^th harmonic voltage from the phase voltage of an alternator. The coils should be short-pitched by an electrical angle of

Figure shows the magnetization curves of an alternator at rated armature current, unity power factor and also at no load. The magnetization curve for rated armature current, 0.8 power factor leading is given by

X_d, X_d^' and X_d^" are steady stated-axis synchronous reactance, transient d-axis reactance and sub-transient d-axis reactance of a synchronous machine respectively. Which of the following statements is true?

A star-connected 440 V, 50 Hz alternators has per phase synchronous reactance of 10 Ω. It supplies a balanced capacitive load current of 20 A, as shown in the per phase equivalent circuit of Figure. It is desirable to have zero voltage regulation. The load power factor should be

The electric field $$\overrightarrow E $$ (in volts/metre) at the point $$(1, 1, 0)$$ due to a point charge of $$+1$$ $$\mu C$$ located at $$\left( { - 1,\,1,\,1} \right)$$ (coordinates in metres) is

Given the potential function in free space to be $$V\left( x \right) = \left( {50{x^2} + 50{y^2} + 50{z^2}} \right)$$ volts, the magnitude (in volts /metre) and the direction of the electric field at a point $$\left( {1,\,\, - 1,\,\,1} \right),$$ where the dimensions are in metres, are

The conductors of a $$10$$ $$km$$ long, single phase, two wire line are separated by a distance of $$1.5$$ $$m.$$ The diameter of each conductor is $$1$$ $$cm.$$ If the conductors are of copper, the inductance of the circuit is

A voltage commutated thyristor chopper circuit is shown in fig. The chopper is operated at $$500$$ $$Hz$$ with $$50\% $$ duty ratio. The load takes a constant current of $$20A$$

(a) Evaluate the circuit turn off time for the main thyristor $$T{h_1}$$
(b) Calculate the value of inductor $$L,$$ if the peak current through the main thyristor $$Th,$$ is limited to $$180$$% of the load current.
(c)Calculate the maximum instantaneous output voltage of the chopper

A single - phase full-bridge voltage source inverter feeds a purely inductive load, as shown in figure. when $${T_1},{T_2},\,\,\,\,\,{T_3},{T_4}$$ are power transistors and $${D_1},{D_2},\,{D_3},{D_4}$$ are feedback diodes. The inverter is operated in square-wave mode with a frequency of $$50$$ $$Hz.$$ If the average load current is zero, what is the time duration of conduction of each feedback diode in a cycle?

A half-wave thyristor converter supplies a purely inductive load, as shown in figure. If the triggering angle of the thyristor is $${120^ \circ }$$, the extinction angle will be

$$AC$$ to $$DC$$ circulating current dual converters are operated with the following relationship between their triggering angles $$\left( {{\alpha _1}} \right.$$ and $$\left. {{\alpha _2}} \right).$$

A $$50$$ Hz alternator is rated $$500$$ $$MVA,$$ $$20$$ $$kV,$$ with $${X_d} = 1.0$$ per unit and $$X'{'_d} = 0.2$$ per unit. It supplies a purely resistive load of $$400$$ $$MW$$ at $$20$$ $$kV.$$ The load is connected directly across the generator terminals when a symmetrical fault occurs at the load terminals. The initial rms current in the generator in per units is

A lossless radial transmission line with surge impedance loading

Consider the model shown in figure of a transmission line with a series capacitor at its mid-point. The maximum voltage on the line is at the location

The conductors of a $$10$$ km long, single phase, two wire line are separated by a distance of $$1.5$$ m. The diameter of each conductor is $$1$$ cm. If the conductors are of copper, the inductance of the circuit is

A 132 kV transmission line AB is connected to a cable BC. The characteristic impedances of the overhead line and the cable are 400$$\Omega $$ and 80$$\Omega $$ respectively. Assume that these are purely resistive. A 250 kV switching surge travels from A to B.

(a) Calculate the value of this voltage surge when it first reaches C.

(b) Calculate the value of the reflected component of this surge when the first reflection reaches A.

(c) Calculate the surge current in the cable BC.

A synchronous generator is connected to an infinite bus through a lossless double circuit transmission line. The generator is delivering 1.0 per unit power at a load angle of $${30^0}$$ when a sudden fault reduces the peak power that can be transmitted to 0.5 per unit. After clearance of fault, the peak power that can be transmitted becomes 1.5 per unit. Find the critical clearing angle.

A single line-to-ground fault occurs on an unloaded generator in phase a positive, negative, and zero sequence impedances of the generator are j0.25 p.u., j0.25 p.u., and j0.15 p.u. respectively. The generator neutral is grounded through a reactance of j0.05 p.u. The prefault generator terminal voltage is 1.0 p.u.
(a) Draw the positive, negative, and zero sequence networks for the fault given.
(b) Draw the interconnection of the sequence networks for the fault analysis.
(c) Determine the fault current.

A power system has two generators with the following cost curves
Generator $$1:$$ $${C_1}\left( {{P_{G1}}} \right) = 0.006\,P_{G1}^2 + 8{P_{G1}} + 350$$ (Thousand Rupees/Hour)
Generator $$2:$$ $${C_2}\left( {{P_{G2}}} \right) = 0.006\,P_{G2}^2 + 7{P_{G2}} + 400$$ (Thousand Rupees/Hour)
The generator limits are
$$\eqalign{ & 100\,MW \le {P_{G1}} \le 650\,MW \cr & 50\,MW \le {P_{G2}} \le 500\,MW \cr} $$

A load demand of $$600$$ $$MW$$ is supplied by the generators in an optimal manner. Neglecting losses in the transmission network, determine the optimal generation of each generator.

A power system has two synchronous generators. The Governor-turbine characteristics corresponding to the generators are
P₁ = 50(50 – f), P₂ = 100 (51 – f)
Where f denotes the system frequency in Hz, and P₁ and P₂ are, respectively, the power outputs (in MW) of turbines 1 and 2. assuming the generators and transmission network to be lossless, the system frequency for a total load of 400 MW is

For the $$Y$$-$$bus$$ matrix given in per unit values, where the first, second, third and fourth row refers to bus $$1, 2, 3$$ and $$4$$ respectively, draw the reactance diagram. $$${Y_{bus}} = j\left[ {\matrix{ { - 6} & 2 & {2.5} & 0 \cr 2 & { - 10} & {2.5} & 4 \cr {2.5} & {2.5} & { - 9} & 4 \cr 0 & 4 & {4 - 8} & {} \cr } } \right]$$$

A $$75$$ MVA, $$10$$ kV synchronous generator has X_d $$= 0.4$$ p.u. The X_d value (in p.u.) is a base of $$100$$ MVA, $$11$$ kV is

Given the relationship between the input $$u(t)$$ and the output $$y(t)$$ to be
$$y\left( t \right) = \int\limits_0^t {\left( {2 + t - \tau } \right){e^{ - 3\left( {t - \tau } \right)}}} u\left( \tau \right)d\tau $$
the transfer function $$Y\left( s \right)/U\left( s \right)$$ is

Consider the voltage waveform $$V,$$ shown in Fig. Find.
$$(a)$$$$\,\,\,\,\,\,\,\,$$ the dc component of $$V,$$
$$(b)$$$$\,\,\,\,\,\,\,\,$$ the amplitude of the fundamental component of $$V,$$ and
$$(c)$$$$\,\,\,\,\,\,\,\,$$ the $$rms$$ value of the ac part of $$V$$