Assuming the operational amplifier to be ideal, the gain $${V_{out}}/{V_{in}}$$ for the circuit shown in figure

The circuit of fig shows a $$555$$ Timer $$IC$$ connected as an Astable multivibrator. The value of the capacitor $$C$$ is $$10$$ $$nF.$$ The values of the resistors $${R_A}$$ and $${R_B}$$ for a frequency of $$10$$ $$kHz$$ and a duty cycle of $$0.75$$ for the output voltage waveform are

The variation of drain current with gate-to-source voltage $$\left( {{{\rm I}_D} - {V_{GS}}} \right.$$ characteristic$$\left. \, \right)$$ of a MOSFET is shown in Figure. The MOSFET is

In the circuit of figure shown, assume that the transistor has $${h_{fe}} = 99$$ and $${V_{BE}} = 0.7V.$$
The value of collector current $${{\rm I}_C}$$ of the transistor is approximately

In the circuit shown, the current gain $$'\beta '$$ of the ideal transistor is $$10.$$ The operating point of the transistor $$\left( {{V_{CE}},{{\rm I}_C}} \right)$$ is

For the circuit shown in figure with an ideal operational amplifier, the maximum phase shift of the output $${V_o}$$ with reference to the input $${V_{in}}$$ is

For the $$n$$-channel enhancement $$MOSFET$$ shown in figure,, the threshold voltage $${V_{th}}\,\, = \,\,2V.$$ The drain current $${I_D}$$ of the $$MOSFET$$ is $$4$$ $$mA$$ when the drain resistance $${R_D}$$ is $$1k\Omega .$$ If the value of $${R_D}$$ is increased to $$4\Omega ,$$ drain current $${I_D}$$ will become

A voltage signal $$\,10\,\,\sin \,\omega t\,\,$$ is applied to the circuit with ideal diodes, as shown in figure. The maximum and minimum values of the output waveform of the circuit are respectively

The following equation defines a separately exited $$dc$$ motor in the form of a differential equation $${{{d^2}\omega } \over {d{t^2}}} + {{B\,d\omega } \over {j\,\,dt}} + {{{K^2}} \over {LJ}}\omega = {K \over {LJ}}{V_a}$$

The above equation may be organized in the state space form as follows
$$\left( {\matrix{ {{{{d^2}\omega } \over {d{t^2}}}} \cr {{{d\omega } \over {dt}}} \cr } } \right) = P\left( {\matrix{ {{{d\omega } \over {dt}}} \cr \omega \cr } } \right) + Q{V_a}$$

where the $$P$$ matrix is given by

A lead compensator used for a closed loop controller has the following transfer function $${\textstyle{{K\left( {1 + {s \over a}} \right)} \over {\left( {1 + {s \over b}} \right)}}}\,\,\,$$ For such a lead compensator

A second order system starts with an initial condition of $$\left( {\matrix{ 2 \cr 3 \cr } } \right)$$ without any external input. The state transition matrix for the system is given by $$\left( {\matrix{ {{e^{ - 2t}}} & 0 \cr 0 & {{e^{ - t}}} \cr } } \right).$$ The state of the system at the end of $$1$$ second is given by.

The roots of the closed loop characteristic equation of the system shown in fig is

A control system is defined by the following mathematical relationship $$${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 5x = 12\left( {1 - {e^{ - 2t}}} \right)$$$

The response of the system as $$\,t \to \infty $$ is

The block diagram shown in fig given is a unity feedback closed loop control system. The steady state error in the response of the above system to unit step input is

The asymptotic Bode plot of the transfer function $${K \over {1 + {s \over a}}}$$. The error in phase angle and $$dB$$ gain at a frequency of $$\omega = 0.5a$$ are respectively

The block diagram of a control system is shown in Fig. The transfer function $$G(s) = Y(s)/U(s)$$ of the system is

The loop gain $$GH$$ of a closed loop system is given by the following expression $${K \over {s\left( {s + 2} \right)\left( {s + 4} \right)}}.$$ The value of $$K$$ for which the system just becomes unstable is

A control system with certain excitation is governed by the following mathematical equation $$${{{d^2}x} \over {d{t^2}}} + {1 \over 2}{{dx} \over {dt}} + {1 \over {18}}x = 10 + 5{e^{ - 4t}} + 2{e^{ - 5t}}$$$
The natural time constants of the response of the system are

The simplified block diagram of a $$10$$-bit $$A/D$$ converter of dual slope integrator type is shown in Fig. The $$10$$-bit counter at the output is clocked by a $$1$$ $$MHz$$ clock. Assuming negligible timing overhead for the control logic, the maximum frequency of the analog signal that can be converted using this $$A/D$$ converter is approximately. Input sample to be converter

The following program is written for an $$8085$$ microprocessor to add two bytes located at memory addresses $$1FFE$$ and $$1FFF$$
$$\eqalign{ & LXI\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,H,\,\,\,1FFE \cr & MOV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B,\,\,\,M \cr & INR\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,L \cr & MOV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,A,\,\,\,M \cr & ADD\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B \cr & INR\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,L \cr & MOV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,M,\,\,\,A \cr & XRA\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,A \cr} $$

On completion of the execution of the program, the result of additional is found.

The Boolean expression $$X\overline Y Z + XYZ + \overline X Y\overline Z + \overline X \overline Y Z + XY\overline Z $$ can be simplified to

Figure shows a $$4$$ to $$1$$ $$MUX$$ to be used to implement the sum $$S$$ of a $$1$$-bit full adder with input bits $$P$$ and $$Q$$ and the carry input $${C_{in}}.$$ Which of the following combinations of inputs to $${{\rm I}_0},\,\,{{\rm I}_1},\,\,{{\rm I}_2}$$ and $$\,\,{{\rm I}_3}$$ of the $$MUX$$ will realize the sum $$S$$?

The shift register shown in Fig. is initially loaded with the bit pattern $$1010.$$ Subsequently the shift register is clocked, and with each clock pulse the pattern gets shifted by one bit position to the right. With each shift, the bit at the serial input is pushed to the left most position $$(MSB).$$ After how many clock pulses will the content of the shift register become $$1010$$ again?

In Fig. the value of $$R$$ is

The $$h$$ $$-$$ parameters for a two $$-$$ port network are defined by
$$\left[ {\matrix{ {{E_1}} \cr {{{\rm I}_2}} \cr } } \right] = \left[ {\matrix{ {{h_{11}}} & {{h_{12}}} \cr {{h_{21}}} & {{h_{22}}} \cr } } \right]\left[ {\matrix{ {{{\rm I}_1}} \cr {{E_2}} \cr } } \right].$$
For the two $$-$$ port network shown in Fig. the value of $${h_{12}}$$ is given by

Fig. shows the waveform of the current passing through an inductor of resistance $$1\,\Omega $$ and inductance $$2$$ $$H.$$ The energy absorbed by the inductor in the first four seconds is

A balanced delta connected load of $$\left( {8 + j6} \right)$$ $$\Omega $$ per phase is connected to a $$400V,$$ $$50Hz,$$ $$3-$$ phase supply lines. If the input power factor is to be improved to $$0.9$$ by connecting a bank of star connected capacitors, the required $$kV$$ $$AR$$ of the bank is

In the circuit shown in Fig., the switch $$S$$ is closed at time $$t=0$$. The voltage across the inductance at $$t = {0^ + },$$ is

Two ac sources feed a common variable resistive load as shown in Fig. Under the maximum power transfer condition, the power absorbed by the load resistance $${R_L}$$ is

In the Fig. $${Z_1} = 10\angle - {60^ \circ },\,\,{Z_2} = 10\angle {60^ \circ },\,$$ $${Z_3} = 50\angle {53.13^ \circ }.\,\,$$ Thevenin's impedance seen from $$X-Y$$ is

In Fig. the potential difference between points $$P$$ and $$Q$$ is

In the circuit of Fig. the magnitudes of $${V_L}$$ and $${V_C}$$ are twice that of $${V_R}$$. The inductance of the coil is

A segment of a circuit is shown in figure. $${v_R} = 5\,\,V,\,\,{v_C} = 4\sin 2t.$$ The voltage $${V_L}$$ is given by

List $$-$$ $${\rm I}$$ represents the figures obtained on a $$CRO$$ screen when the voltage signals $$\,{V_X}\,\, = \,\,{V_{Xm}}\sin \,\,\omega t\,\,$$ and $$V_y^ \cdot \,\, = \,\,{V_{ym}}\sin \,\,\left( {\omega t + \Phi } \right)\,\,$$ are given to its $$X$$ and $$Y$$ plates respectively and $$\Phi $$ is changed. Choose the correct value of $$\Phi $$ from List $$-$$ $${\rm I}$$ to match with the corresponding figure of List $$-$$ $${\rm II}$$.

The simplified block diagram of a $$10$$bit A/D converter of dual slope integrator type is shown in fig. The $$10$$-bit counter at the output is clocked by a $$1MHz$$ clock. Assuming negligible timing overhead for the control logic, the maximum frequency of the analog signal that can be converted using this A/D converter is approximately.

An ac voltmeter uses the circuit shown below, where the $$PMMC$$ meter has an internal resistance of $$100$$$$\Omega $$ and requires a dc current of $$1$$ $$mA$$ for full scale deflection. Assuming the diodes to be ideal, the value of $${R_s}$$ to obtain full scale deflection with $$100$$ $$V$$ (ac rms) applied to the input terminal would be

The inductance of a certain moving-iron ammeter is expressed as $$L = 10 + 3\theta - {{{\theta ^2}} \over 4}\mu H,\,\,$$ where $$\,\,\theta \,\,\,$$ is the deflection in radians from the zero position. The control spring torque in $$\,\,25\,\, \times \,\,{10^{ - 6}}\,\,\,$$ Nm/radian. The deflection of the pointer in radian when the meter carries a current of $$5A,$$ is

A wattmeter reads $$400$$ $$W$$ when its current coil is connected in the $$R$$ phase and its pressure coil is connected between this phase and the neutral of a symmetrical $$3$$-phase system supplying a balanced star connected $$0.8$$ $$p.f.$$ inductive load. The phase sequence is $$RYB.$$ What will be the reading of this wattmeter if its pressure coil alone is reconnected between the $$B$$ and $$Y$$ phases, all other connections remaining as before?

The items in List $$-$$ $${\rm I}$$ represent the various types of measurements to be made with a reasonable accuracy using a suitable bridge. The items in List $$-$$ $${\rm II}$$ represent the various bridges available for this purpose. Select the correct choice of the item in List $$-$$ $${\rm II}$$ for the corresponding item in List $$-$$ $${\rm I}$$ from the following.

List $$-$$ $${\rm I}$$
$$A.$$ Resistance in the milli Ohm range
$$B.$$ Low values of Capacitance
$$C.$$ Comparison of resistances which are nearly equal
$$D.$$ Inductance of a coil with a large time $$-$$ constant

List $$-$$ $${\rm II}$$
$$1.$$ Wheatstone Bridge
$$2.$$ Kelvin Double Bridge
$$3.$$ Schering Bridge
$$4.$$ Wien's Bridge
$$5.$$ Hay's Bridge
$$6.$$ Carry $$-$$ Foster Bridge

A $$500$$ $$A/5$$ $$A,$$ $$50$$ $$Hz$$ current transformer has a bar primary. The secondary burden is a pure resistance of $$1\,\Omega $$ and it draws a current of $$5A$$. If the magnetic core requires $$250$$ AT for magnetization, the percentage ratio error is

The voltage-flux adjustment of a certain $$1$$-phase $$220$$ $$V$$ induction watt-hour meter is altered so that the phase angle between the applied voltage and the flux due to it $${85^0}$$ (instead of $${90^0}$$). The errors introduced in the reading of this meter when the current is $$5$$ $$A$$ at power factors of unity and $$0.5$$ lagging are respectively

A Manganin swamping resistance is connected in series with a moving coil ammeter consisting of a milli-ammeter and a suitable shunt in order to

The effect of stray magnetic fields on the actuating torque of a portable instrument is maximum when the operating field of the instrument and the stray fields are

A $$4$$-pole, $$3$$-phase, double layer winding is housed in a $$36$$-slot stator for an $$ac$$ machine with $$60$$ degree phase spread. Coil span is $$7$$ slot pitches. Number of slots in which top and bottom layers belong to different phases is.

Curves X and Y in Figure denote open circuit and full-load zero power factor (zpf) characteristics of asynchronous generator. Q is a point on the zpf characteristics at 1.0 p.u. voltage. The vertical distance PQ in Figure gives the voltage drop across

A stand-alone engine driven Synchronous generator is feeding a partly inductive load. A capacitor is now connected across the load to completely nullify the inductive current. For this operating condition.

Following are some of the properties of rotating electrical machines
P. Stator winding current is dc, rotor-winding current is ac
Q. Stator winding current is ac, rotor-winding current is dc
R. Stator winding current is ac, rotor-winding current is ac
S. Stator has salient poles and rotor has commutator
T. Rotor has salient poles and sliprings and stator is cylindrical
U. Both stator and rotor have poly-phase windings

DC machines. Synchronous machines and Induction machines exhibit some of the above properties as given in the following table. Indicate the correct combination from this table

When Stator and Rotor windings of a 2-pole rotating electrical machine are excited, each would produce a sinusoidal mmf distribution in the air gap with peak values F_s and F_r respectively. The rotor mmf lags stator mmf by a space angle $$\delta\;$$ at any instant as shown in Fig. Thus, half of stator and rotor surfaces will form one pole with the other half forming the second pole. Further, the direction of torque acting on the rotor can be clockwise or counter-clockwise. The following Table gives four sets of statements as regards poles and torque. Select the correct set corresponding to the mmf axes as shown in Figure.

A 3-phase Inductor Motor is driving a constant torque load at rated voltage and frequency. If both voltage and frequency are halved, following statements relate to the new condition if stator resistance, leakage reactance and core loss are ignored.
P. The difference between synchronous speed and actual speed remains same
Q. The air-gap flux remains same
R. The stator current remains same
S. The p.u. slip remains same
Among the above, correct statements are

A single phase induction motor with only the main winding excited would exhibit the following response at synchronous speed

Figure shows a $$\triangle$$ - Y connected 3-phase distribution transformer used to step down the voltage from 11000 V to 415 V line-to line. It has two switches S₁ and S₂. Under normal conditions S₁ is closed and S₂ is open. Under certain special conditions S₁ is open and S₂ is closed. In such a case the magnitude of the voltage across the LV terminals a and c is

A single phase transformer has a maximum efficiency of 90% at full load and unity power factor. Efficiency at half load at the same power factor is

A dc series motor driving an electric train faces a constant power load. It is running at rated speed and rated voltage. If the speed has to be brought down to 0.25 p.u. the supply voltage has to be approximately brought down to

Figure shows an ideal single-phase transformer. The primary and secondary coils are wound on the core as shown. Turns ratio $$\left(\frac{N_1}{N_2}\right)$$=2. The correct phasors of voltages $$E_1,\;E_2$$ currents $$I_1,\;I_2$$ and core flux $$\phi$$ are as shown in

Figure shows an ideal three-winding transformer. The three windings 1,2,3 of the transformer are wound on the same core as shown. The turn's ratio N₁:N₂:N₃ is 4:2:1. A resistor of 10 Ω is connected across winding-2. A capacitor of reactance 2.5 Ω is connected across winding-3. Winding-1 is connected across a 400 V, ac supply. If the supply voltage phasor $$\overline V=400\angle0^\circ$$, the supply current phasor $${\overline I}_1$$ is given by

No-load test on a 3-phase induction motor was conducted at different supply voltages and a plot of input power versus voltage was drawn. This curve was extrapolated to intersect the y-axis. This intersection point yields

Group I lists different applications and Group II lists the motors for these applications. Match the application with the most suitable motor and choose the right combination among the choices given there after:

Group I
P. Food mixer
Q. Cassette tape recorder
R. Domestic water pump
S. Escalator

Group II
1. Permanent magnet dc motor
2. Single phase induction motor
3. Universal motor
4. Three phase induction motor
5. DC series motor
6. Stepper motor

Two conductors are carrying forward and return current of $$ + {\rm I}$$ and $$ - {\rm I}$$ as shown in Fig.

The magnetic field intensity $$\overrightarrow H $$ at point $$P$$ is

A point charge of $$+1$$ $$nC$$ is placed in a space with a permittivity of $$8.85 \times {10^{ - 12}}\,F/m$$ as shown in Fig. The potential difference $${V_{PQ}}$$ between two points $$P$$ and $$Q$$ at distance of $$40mm$$ and $$20$$ $$mm$$ respectively from the point charge is

A parallel plate capacitor has an electrode area of $$100$$ $$m{m^2}$$, with a spacing of $$0.1$$ $$mm$$ between the electrodes. The dielectric between the plates is air with a permittivity of $$8.85 \times {10^{ - 12}}\,\,F/m.$$ The charge on the capacitor is $$100$$ $$V$$. The stored energy in the capacitor is

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness ($${t_1}$$ and $${t_2}$$) as shown in Fig. The two different dielectric materials are separated by a conducting foil $$F.$$ The voltage of the conducting foil is

A chopper is employed to charge a battery as shown in figure. The charging current is $$5A$$. The duty ratio is $$0.2.$$ The chopper output voltage is also shown in figure. The peak to peak ripple current in the charging current is

An inverter has a periodic output voltage with the output waveform as shown in figure

When the conduction angle $$\alpha = {120^0},$$ the $$rms$$ fundamental component of the output voltage is

An inverter has a periodic output voltage with the output waveform as shown in figure

With reference to the output waveform given in figure, the output of the converter will be free form $${5^{th}}$$ harmonic when

A fully controlled natural commuted $$3$$-phase bridge rectifier is operating with a firing angle $$\alpha = {30^0}.$$ The peak to peak voltage ripple expressed as a ratio of the peak output $$dc$$ voltage at the output of the converter bridge is

A phase - controlled half - controlled single - phase converter is shown in figure. The control angle $$\alpha = {30^ \circ }$$

The output $$dc$$ voltage wave shape will be as shown in

Figure shows a thyristor with the standard terminations of anode $$(A),$$ cathode $$(K),$$ gate $$(G)$$ and the different junctions named $$J1, J2,$$ and $$J3$$. When the thyristor is turned on and conducting

Figure shows a $$MOSFET$$ with an integral body diode. It is employed as a power switching device in the ON and OFF states through appropriate control. The ON and OFF states of the switch are given on the $${V_{DS}} - {{\rm I}_s}$$ plane by

A $$3$$-phase, $$11$$-$$kV$$ generator feeds power to a constant power unity power factor load of $$100$$ $$MW$$ through a $$3$$-phase transmission line. The line-to-line voltage at the terminals of the machine is maintained constant at $$11$$ $$kV$$. The per unit positive sequence impedance of the line based on $$100$$ $$MVA$$ and $$11$$ $$kV$$ is $$j$$ $$0.2$$. The line to line voltage at the load terminals is measured to be less than $$11$$ $$kV$$. The total reactive power to be injected at the terminals of the load to increase the line-to-line voltage at the load terminals to $$11$$ $$kV$$ is

In a transmission line each conductor is at $$20$$ $$kV$$ and is supported by a string of $$3$$ suspension insulators. The air capacitance between each cap-pin junction and tower is one-fifth of the capacitance $$C$$ of each insulation unit. A guard ring, effective only over the line-end insulator unit is fitted so that the voltages on the two units nearest the line-end are equal.

(a) Calculate the voltage on the line-end unit.
(b) Calculate the value of capacitance $${C_x}$$ required.

Bundled conductors are mainly used in high voltage overhead transmission lines to

A generator delivers power of 1.0 p.u. to an infinite bus through a purely reactive network. The maximum power that could be delivered by the generator is 2.0 p.u. A three-phase fault occurs at the terminals of the generator which reduces the generator output to zero. The fault is cleared after $${t_c}$$ seconds. The original network is then restored. The maximum swing of the rotor angle is found to be $${\delta _{\max }} = 110$$ electrical degree. Then the rotor angle in electrical degrees at $$t = {t_c}$$ is

Incremental fuel costs (in some appropriate unit) for a power plant consisting of three generating units are
$${\rm I}{C_1} = 20 + 0.3\,\,{P_1},\,{\rm I}{C_2} = 30 + 0.4\,\,{P_2},\,{\rm I}{C_3} = 30$$
Assume that all the three units are operating all the time. Minimum and maximum loads on each unit are $$50$$ $$MW$$ and $$300$$ $$MW$$ respectively. If the plant is operating on economic load dispatch to supply the total power demand of $$700$$ $$MW$$, the power generated by each unit is

A balanced delta connected load of $$\left( {8 + j6} \right)\Omega $$ per phase is connected to a $$400$$ $$V$$, $$50$$ $$Hz$$, $$3-$$phase supply lines. If the input power factor is to be improved to $$0.9$$ by connecting a bank of star connected capacitors the required KVAR of the bank is

The ABCD parameters of a $$3$$-phase overhead transmission line are $$\,A = D = 0.9\angle {0^ \circ }.\,\,B = 200\,\angle {90^ \circ }\,\,\Omega \,\,\,$$ and $$\,\,C = 0.95\, \times \,\,{10^{ - 3}}\angle {90^ \circ }\,\,S.\,\,\,\,$$ At no-load condition, a shunt inductive reactor is connected at the receiving end of the line to limit the receiving end voltage to be equal to the sending-end voltage. The ohmic value of the reactor is

A round rotor generator with internal voltage $${E_1} = 2.0\,\,$$ p.u.and $$\,X = 1.1\,\,$$ p.u. is connected to a round rotor synchronous motor with internal voltage $$\,\,{E_2} = 1.3\,\,$$ p.u. and $$\,X = 1.2\,\,$$ p.u. The reactance of the line connecting the generator to the motor is $$0.5$$ p.u. when the generator supplies $$0.5$$ p.u. power, the rotor angle difference between the machines will be

A dc distribution system is shown in figure with load currents as marked. The two ends of the feeder are fed by voltage sources such that $${V_P} - {V_Q} = 3V.$$ the value of the voltage $${V_P}$$ for a minimum voltage of $$220$$ $$V$$ at any point along the feeder is

A list of relays and the power system components protected by the relays are given in List-$${\rm I}$$ and List-$${\rm II}$$ respectively. Choose the correct match from the four choices given below

List-$${\rm I}$$
$$A.$$ Distance relay
$$B.$$ Under frequency relay
$$C.$$ Differential relay
$$D.$$ Buchholz relay

List-$${\rm II}$$
$$1.$$ Transformers
$$2.$$ Turbines
$$3.$$ Busbars
$$4.$$ Shunt capacitors
$$5.$$ Alternators
$$6.$$ Transmission lines

The bus impedance matrix of a $$4$$-bus power system is given by $$${Z_{bus}} = \left[ {\matrix{ {j0.3435} & {j0.2860} & {j0.2723} & {j0.277} \cr {j0.2860} & {j0.3408} & {j0.2586} & {j0.2414} \cr {j0.2723} & {j0.2586} & {j0.2791} & {j0.2209} \cr {j0.2277} & {j0.2414} & {j0.2209} & {j0.2791} \cr } } \right]$$$

A branch having an impedance of $$j0.2\Omega $$ is connected between bus $$2$$ and the reference. Then the values of $${Z_{22,new}}$$ and $${Z_{23,new}}$$ of the bus impedance matrix of the modified network are respectively

The interrupting time of a circuit breaker is the period between the instant of

A power system consists of $$300$$ buses out of which $$20$$ buses are generator buses, $$25$$ buses are the ones with reactive power support and $$15$$ buses are the ones with fixed shunt capacitors. All the other buses are load buses. It is proposed to perform a load flow analysis for the system using Newton-Raphson method. The size of the Newton-Raphson Jacobian matrix is

Choose two appropriate auxiliary components of a HVDC transmission system from the following
$$1.$$ D.C. line inductor
$$2.$$ A.C. line inductor
$$3.$$ Reactive power sources
$$4.$$ Distance relays on D.C. line
$$5.$$ Series capacitance of A.C. line

A three-phase alternator generating unbalanced voltages is connected to an unbalanced load through a 3-phase transmission line as shown in figure. The neutral of the alternator and the star point of the load are solidly grounded. The phase voltages of the alternator are
$${E_a} = 10\angle {0^ \circ }V,\,\,\,{E_b} = 10\angle - {90^ \circ }V,\,\,{E_c} = 10\angle {120^ \circ }\,\,V.\,\,\,\,$$ The positive sequence component of the load current is

A 20-MVA, 6.6-kV, 3-phase alternator is connected to a 3-phase transmission line. The per unit positive sequence, negative sequence and zero sequence impedance of the alternator are j0.1, and j0.04 respectively. The neutral of the alternator is connected to ground through an inductive reactor of j0.05 p.u. The per unit positive, negative and zero sequence impedances of the transmission line are j0.1 and j0.3 respectively. All per unit values are based on the machine ratings. A solid ground fault occurs at one phase of the far end of the transmission line. The voltage of the alternator neutral with respect to ground during the fault is

A surge of 20 kV magnitude travels along a lossless cable towards its junction with two identical lossless overhead transmission lines. The inductance and the capacitance of the cable are 0.4 mH and 0.5 $$\mu F$$ per km. The inductance and capacitance of the overhead transmission lines are 1.5 mH and 0.015 $$\mu F$$ per km. The magnitude of the voltage at the junction due to surge is