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Statics and Dynamics By R. Hibbeler Book April Punmia, Ashok Kumar Jain, Arun April 8. April 7. Common D MCQ 1. The coils are to be connected to obtain a single-phase. Coil-1 is excited with single phase. The transformers are connected in the following manner: Which of the options given should be exercised to realize the required auto-transformer?

A Connect A and D. Both the coils have a rated current of 25 A. The following wattmeters are available in a laboratory: If the rotor resistance at standstill is 7. The air-gap power of the motor will be A Low Power Factor W2: High Power Factor W4: The friction and windage losses are W and the core losses are W.

The stator and rotor copper losses are 1. Low Power Factor W3: A 3-phase. The stator line-to-line voltage rms and frequency to obtain the maximum torque at starting will be: Two-wattmeter method is used to measure the input power to induction motor. A synchronous motor is connected to an infinite bus at 1. Its synchronous reactance is 1. The armature resistance is 0. A V. The operating power factor will become A 0. If its shaft load is reduced by half. The per unit saturated synchronous reactance is A 1.

C and D. The short circuit armature current at a field current of 10 A is equal to the rated armature current. Out of the operating points A. The value of slip for maximum torque is A A In an open circuit test.

Neglect the stator resistance and rotational losses. A Compensating winding is used for neutralizing armature reaction while interpole winding is used for producing residual flux B Compensating winding is used for neutralizing armature reaction while interpole winding is used for improving commutation C Compensating winding is used for improving commutation while interpole winding is used for neutralizing armature reaction D Compensation winding is used for improving commutation while interpole winding is used for producing residual flux YEAR TWO MARKS A V DC machine supplies 20 A at V as a generator.

The rating of the first transformer is kVA ratings. If the rating of second transformer is kVA. At rated frequency of 50 Hz and rated voltage of V its speed is rpm. Find the speed at 30 Hz. The rating of the first transformer is kVA and its pu leakage impedance is 0.

The armature nodia. Neglect all losses and consider linear magnetic circuit. The fundamental flux per pole is 0. No Load Test: A 4-pole. Its no load and blocked rotor test data are given below. Each coil has 10 turns and is short pitched by an angle to 36c electrical. What will be the new load in percent. Identify the correct statement regarding the polarity of the induced emf at this instant in coil sides c1 and c2.

Y and Z. X'2 and magnetizing reactance XM. Which one of them represents the operation at a slip greater than 1? Consider the instant when the poles are in a position as shown. A the speed decreases and the stator current increases B both the speed and the stator current decreases C the speed and the stator current remain practically constant D there is negligible change in the speed but the stator current decreases MCQ 1. Armature emf E 1.

C Short circuit ratio is the ratio of the field current required to produces the rated voltage on open circuit to the rated armature current. Ia and w only 5. Ia only Codes: D The V-cure of a synchronous motor represents the variation in the armature current with field excitation. If the starting current drawn is 6 times the full load current. B The damper bars help the synchronous motor self start. Developed torque T 2. Flux f. A In salient pole machines. Reason [R]: The percentage load at which the transformer is expected to have maximum efficiency is A Neglect the armature resistance and consider operation at full load and unity power factor.

For counter clockwise rotation of the motor. The nominal rating of the auto. The efficiency of the motor while it is operating on load at rpm drawing a current of 3. The phase impedance of the transformer referred to the primary is A 0. Y distribution transformer are 0. At no load. Y-connected induction motor has full load slip of nodia.

The machine is running at rpm. DC generator has a simplex wave-wound armature containing 32 coils of 6 turns each. The friction and windage losses are 2 kW and the core loss is 0. Its flux per pole is 0. The line voltage of the first machine is adjusted to V and that of the second machine is adjusted to V. Y-connected synchronous generator has a rated voltage of The output torque of the machine at full load is A 1.

The line current drawn is A Y-connected alternators are to be paralleled to a set of common busbars. The armature has a per phase synchronous reactance of 1. Under this condition. The machine voltages are in phase at the instant they are paralleled. The line current when operating at full load rated conditions will be A The shaft is supplying 9 kW load at a power factor of 0.

Q is a point on the zpf characteristics at 1. Escalator 4. A the field current and fuel input have to be reduced B the field current and fuel input have to be increased C the field current has to be increased and fuel input left unaltered D the field current has to be reduced and fuel input left unaltered MCQ 1. For this operating condition. Single-phase induction motor R. Permanent magnet dc motor Q Cassette tape recorder 2.

Efficiency at half load at the same power factor is A DC series motor 6. Food mixer 1. This curve was extrapolated to intersect the y-axis. Stepper motor Codes: Three-phase induction motor 5. Universal motor S.

Domestic water pump 3. Match the application with the most suitable motor and choose the right combination among the choices given thereafter Group-I Group-II P. A capacitor is now connected across the load to completely nullify the inductive current. The primary and secondary coils are wound on the core as shown.

It has two switches S1 and S 2. I2 and core flux F are as shown in nodia. The armature of generator is connected to a load resistance. With rated voltage across the motor. Armature reaction and mechanical losses can be neglected.

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Under certain special conditions S1 is open and S 2 is closed. The field of the generator is also connected to the same supply source as the motor. The p. The correct phasors of voltages E1. Under normal conditions S1 is closed and S 2 is open. Y connected. Stator has salient poles and rotor has commutator.

Stator winding current is ac. Synchronous machines and Induction machines exhibit some of the above properties as given in the following table. Winding-1 is connected across a V.

The turns ratio N1: N3 is 4: A resistor of 10 W is connected across winding Rotor has salient poles and sliprings and stator is cylindrical. Both stator and rotor have poly-phase windings. DC machines. A capacitor of reactance 2. Stator winding current is dc. The three windings 1. T MCQ 1. The rotor mmf lags stator mmf by a space angle d at any instant as shown in figure.

Coil span is 7 short pitches. If the speed has to be brought down to 0. Select the correct set corresponding to the mmf axes as shown in figure. It is running at rated speed and rated voltage. If both voltage and frequency are halved. The difference between synchronous speed and actual speed remains same 2. The airgap flux remains same 3. The stator current remains same 4. Which one of the following quantities will not be sinusoidal? A resistive load is connected to the low voltage winding which draws rated current.

The torque-speed characteristic of this motor will be approximately represented by which curve of figure? The reading of the voltmeter. The transformer has 12 and 99 turns in the low and high voltage windings respectively. Find the steady state speed at which the motor will drive the load and the armature current drawn by it from the source. Assuming no load losses to be zero.

The short circuit reactance of system A and B are 0. If no power is transferred between A and B. The motor is connected to V dc supply and rated dc voltage is applied to the field winding. If the armature drawn 5 A from the source. Rated dc voltage is applied to both the armature and field winding of the motor. A and B as shown in figure. When the stator is connected to the rated supply with the field excitation unchanged. Neglect the winding resistance and core losses of the transformer.

Neglect the rotational losses of the machine. The magnetizing reactance of the transformer referred to the high voltage side is W. The leakage reactance of the high and low voltage windings are 1. The approximate average no load steady state speed when this motor is connected to V. The mechanical load on the motor is now increased till the stator current is equal to 50 A. The field excitation remains unchanged. The machine is connected to the V.

Find the speed at which the machine is running. Y-connected supply is connected to a balanced three-phase Y-connected load. At a particular field excitation. Also find the torque developed by the machine.

Which of the following statements is true? It is found that the magnitude of the stator current is equal to the rated current of the machine but the machine is running at a speed higher than its rated speed. Xld and X md are steady state d -axis synchronous reactance. If the instantaneous phase-a of the supply voltage is V cos wt and the phase-a of the load current is I cos wt.

When the armature is short-circuited and the rated armature current of 10 A is passed through it. If the flux remains constant.

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The series field resistance is 0. Neglect the losses in the driving motor. Sketch the shape nodia. Initially the machines are sharing load equally.

On open-circuiting the armature with rated excitation. The primary of the transformer is energized with an ideal current source. When the excitation is not switched on.

If the flux at an armature current of 20 A is 0. Reasonable approximations may be made. Leakage flux in an induction motor is flux that linked the stator winding or the rotor winding but not both. The angle d in the swing equation of a synchronous generator is the angular displacement of an axis fixed to the rotor with respect to a synchronously rotating axis.

For the given transformer. Let subscript 1 is used for first transformer and 2 is used for second transform. Since the core length of the second transformer is 2 times of the first. Given that magnetizing current and losses are to be neglected. Locked rotor line current.

If the full supply voltage is applied to the motor. A 4-point starter is used to start and control speed of a dc shut motor. The Back emf will go to zero when field is reduced. An air-core transformer has linear B -H characteristics. But when Field increases though in reverse direction the back emf will cause the current to reduce.

A variable resistance should be connected in series with the armature resistance to limit the starting current. Eb Ra at the time of starting. Load torque. Given single-phase iron core transformer has both the vertical arms of cross section area 20 cm2. So B is un-stable. Given 3-phase squirrel cage induction motor. So A is stable. At point A if speed -. Torque - speed. SOL At point B if speed. Star connected synchronous motor. When both S1 and S2 open. Since S2 closed and S1 open.

Given 3-phase. High Power Factor In one circuit test the wattmeter W2 is used and in short circuit test of transformer W3 is used. In case the motor is unexcited. The residual magnetism in the permanent magnetic material produced. N2 dt df During. Transformer connection will be represented by Y d1. The detent torque is defined as the maximum load torque that can be applied to the shaft of an unexcited motor without causing continuous rotation.

Given 3-f. For max. Given V. In transformer zero voltage regulation at full load gives leading power factor. External Resistance to be added in the armature circuit to limit the armature nodia. Reactance is 1. When the 3-f synchronous motor running at full load and unity power factor and shaft load is reduced half but field current is constant then it gives leading power factor.

Given star connected synchronous machine. Given starting torque is The two windings are displaced 90c in space. In transformer. A synchronous generator is feeding a zero power factor lagging load at rated current then the armature reaction is demagnetizing. Interpoles generate voltage necessary to neutralize the e.

DC machine. Interpoles have a polarity opposite to that of main pole in the direction of rotation of armature. A single-phase capacitor start induction motor. It has cage rotor and its stator has two windings. The direction of rotation can be changed by reversing the main winding terminals. In DC motor. Rating of second transformer is kVA actual impedance So.

Given speed of a 4-pole induction motor is controlled by varying the supply frequency when the ratio of supply voltage and frequency is constant. Given that: Three phase star delta connection of transformer induces a phase difference of 30c between output and input line voltage. At c1 the emf induced upward and no emf induced at c2 and c2l SOL 1. For an induction motor the ratio of gross power output to air-gap is equal to 1.

Given that two magnetic pole revolve around a stationary armature. Given A 50 kW DC shunt motor is loaded. So at point W slip is greater than 1. The leakage reactances X1. In synchronous machine, when the armature terminal are shorted the field current should first be decreased to zero before started the alternator. In open circuit the synchronous machine runs at rated synchronous speed. The field current is gradually increased in steps. The short circuit ratio is the ratio of field current required to produced the rated voltage on open to the rated armature current.

Given a three-phase cage induction motor is started by direct on line switching at rated voltage. The starting current drawn is 6 time the full load current. If the stator voltage drop is neglected the terminal voltage E1. To avoid saturation and to minimize losses motor is operated at rated airgap flux by varying terminal voltage with frequency.

Stepper motor is rotated in steps, when the supply is connected then the torque is produced in it. The higher value of torque is pull out torque and less torque. In this type the capacitor is connected in running condition. Given that if 3-f induction motor is rotated in clockwise then the phase sequence of supply voltage is A-B-C.

In counter clock wise rotation of the motor the phase sequence is change so in the counter clockwise rotation the phase sequence is A-C-B. In linear electromagnetic circuit the field energy is equal to the co-energy.

Given that 8-Pole, 50 Hz induction machine in seventh space harmonic mmf wave. Rotating electrical machines having its self inductance of stator and rotor windings is independent of the rotor position of synchronizing torque.

Given that V, 50 Hz, 4-Pole, capacitor-start induction motor. Given that the armature has per phase synchronous reactance of 1. Given 1. Simplex wave wound flux per pole is 0. Given a V, 50 Hz and 0. The friction and windage losses are 2 kW and core losses is 0. Given that MW, 3-f star connected synchronous generator has a rated voltage of At full load, load factor is L.

In food mixer the universal motor is used and in cassette tap recorder permanent magnet DC motor is used.

The Domestic water pump used the single and three phase induction motor and escalator used the three phase induction motor. Given a engine drive synchronous generator is feeding a partly inductive load. A capacitor is connected across the load to completely nullify the inductive current.

Then the motor field current has to be reduced and fuel input left unaltered. Given open circuit and full-load zero power factor of a synchronous generator. At point Q the zero power factor at 1. The voltage drop at point PQ is across synchronous reactance. Given no load test on 3-f induction motor, the graph between the input power and voltage drop is shown in figure, the intersection point yield the friction and windage loss.

Option C is correct. The armature resistance in per unit is 0. Given that when the switch S 1 is closed and S 2 is open then the V is step down at V output Second time when the switch S 1 is open and switch S 2 is closed then 2-phase supply is connected to the transformer then the ratio of voltage is. Given that N1: The stator winding is connected to dc supply and rotor winding flows ac current. Induction machines: In induction motor the ac supply is connected to stator winding and rotor and stator are made of poly-phase windings.

Synchronous machines: In this type machines the stator is connected to ac supply but rotor winding is excited by dc supply. The rotor is made of both salient pole and slip rings and stator is made of cylindrical. Given that Fs is the peak value of stator mmf axis. Fr is the peak value of rotor mmf axis. The rotor mmf lags stator mmf by space angle d.

The direction of torque acting on the rotor is clockwise or counter clockwise. When the opposite pole is produced in same half portion of stator and rotor then the rotor moves.

So portion of stator is north-pole in ABC and rotor abc is produced south pole as well as portion surface CDA is produced south pole and. The torque direction of the rotor is clock wise and torque at surface is in counter clockwise direction.

Voltage and frequency are halved and stator resistance, leakage reactance and core losses are ignored. Then the motor synchronous speed and actual speed difference are same. Option A is correct. Than Torque speed characteristics become linear at saturated region. Motor is overloaded. Than Torque is decreased.

A dc series motor driving a constant power load running at rated speed and rated voltage. Given that transformer rating 1 kVA.

In this case voltmeter reading will be zero. Separately Excited dc motor of V. Second case when stator connected to rated supply then terminal voltage decreases and current will lead from the supply voltage. Slip ring induction motor of 5 kW.

First we have to draw its equivalent circuit as nodia. Ne Ns. In transformer protection. Y-connected supply is given to Y-load instantaneous phase-a of supply is V cos wt and load current is I cos wt. For armature controlled separately excited dc motor drive with closed loop speed control. We use inner current loop because inner current loop limits the peak current of motor to the permissible value. Ideal transformer of linear B -H with turn ratio 1: Given nodia.

Given 50 kW of synchronous motor driven by another motor. The voltage at node 3 is 1. If a capacitor having reactance of.

Z 33 of its bus impedance matrix is j0. All the line reactances are equal to j1 W MCQ 1. The fuel cost of generators G1 and G2 are: SD1 and SD2 are complex power demands at bus 1 and bus 2 respectively. The critical clearing angle. The inertia constant of the generator is 5 MW.

The generator no-load voltage is 1. These currents are balanced if f 1 is equal to. G2 and G 3 are of MW capacity each and have identical fuel cost characteristics. The three generators G1. Select the most suitable power evacuation transmission configuration among the following options nodia. The armature resistance is negligible.

Y -bus. VCD 2 0. The current through the operating coils is A 0. B The magnitude of terminal voltage increases. Which of the following may be said about the steady state terminal voltage and field current of the generator? A The magnitude of terminal voltage decreases.

The inter-phase capacitance C1 between each line conductor and the sheath is 0. Y and B in the figure.

The nodia. With the field voltage held constant. C The magnitude of terminal voltage increases. Each of the conductors is suspended by an insulator string having two identical porcelain insulators. The per-phase charging current is A 2.

The impedance diagram is nodia. Ohm Relay b. Short Line 1. Reactance Relay c. List-I List-II a. Long Line 3. Mho Relay A a " 2. Medium Line 2. The details of the generators are Rating Efficiency Regulation Pu.

The inertia constant H will be A 2. Then the percentage ratio of line length to wavelength will be given by A B Directional over current protection set to pick up at 1. There are tow generation G 1 and G 2 in the system with cost curves C1 and C2 respectively defined as follows. Which one of the following transmission line protection schemes will not pick up for this condition? The critical clearing time of circuit breaker is 0.

If the has positive sequence impedance of 15 W and zero sequence impedance of 48 W. The synchronous generator transfers 1. Solve the problems and choose the correct answers. Branches e1. The load current values indicated in the figure are in per unit. A symmetrical three phase fault occurs at centre of the line.

The nature of transformer connections and phase shifts are indicated for all but one transformer Which of the following connections. The optimum generation schedule is: The maximum and minimum generation limits are also indicated. Which of the following statements is true in the steady state: If we neglect the charges on the other phase conductor and ground.

Generator B: The instantaneous line currents and phase to neutral voltages are denoted by ia.

What action should be taken to increase the capacitor dc voltage slowly to a new steady state value. You may neglect all losses and harmonics. Vcn respectively. A Make d positive and maintain it at a positive value B Make d positive and return it to its original value C Make d negative and maintain it at a negative value nodia. The circuit breakers numbered from 1 to 7 are of identical type.

A single line to ground fault with zero fault impedance occurs at the midpoint of the line at point F. If the relays are coordinated correctly. The maximum value of the per unit line reactance. Due to some previous disturbance. T X if Tit is given X: The bus voltage phasors so obtain are indicated on figure A. These two isolated systems are now interconnected by a short transmission line as shown in figure B. Separate load flow solutions are computed individually of the two systems.

X which are initially not interconnected. The value of inductor and capacitor is A One of these loads is programmed to trip permanently if the frequency falls below 48 Hz. If an additional load of 3. A unity power-factor load of 4 kW is connected between phase A and neutral N.

It is desired to achieve zero neutral current through the use of a pure inductor and a pure capacitor in the other two phases. Which one of the following is true for this link? D constants of a kV line are: The shortest and longest distances between the phase and telephone conductors are 2. The load neutral is isolated. The system frequency is 50 Hz. A generator feeds power to an infinite bus through a double circuit transmission line.

The infinite bus voltage is 1 pu. A 3-phase fault occurs at the middle point of one of the lines.

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For a power system the admittance and impedance matrices for the fault studies are as follows. If all the pu calculations are 1 2 with the respective base values. For system base values of 10 MVA and 69 kV in load circuit.

At the receiving end of the line a load is supplied through a step down transformer of 10 MVA. If it is operated at kV with the series reactance unchanged. A solid 3-phase fault takes place at bus 2. The system was unloaded prior to the fault. The rating in kVAR of the delta connected capacitive reactive power bank necessary to bring the pf to unity is nodia.

With usual notations the equivalent A. If the capacitor goes out of service. For most economic generation to meet MW of load P1 and P2 respectively. Given that. C and D constants are obtained. Solve the problems and choose the correct answers At a kV substation of a power system. Neglecting the resistances and suspectances of the system. If one of the double-circuit is tripped.

The infinite bus voltage is maintained at 1. Data for Q. XLPE insulated power cable delivering power at 50 Hz. If the dielectric loss tangent of XLPE is 2 Ignoring the length of the line. It is operating at rated voltage and disconnected from the rest of the system no load.

The generator is operating at no load and rated voltage when a three phase short circuit fault occurs between the breakers and the transformer. The magnitude of initial symmetrical rms current in the breakers will be A 4. The magnitude of the bus voltage Vt of the system in pu will be A 0. In order to produce power at 50 Hz. Generator is Y-connected and its neutral is solidly grounded. The currents in the lines are as shown on the diagram.

Neglect losses and assume constant power input to the shaft. The magnitude of the sub-transient line current for single line to ground fault at the generator terminal in pu will be A 2. The accelerating torque in the generator in MNm at the time of fault will be A 1.

It is proposed to perform a load flow analysis in the system using Newton-Raphson method. C line T. C line inductor R. When the generator supplies 0. All the other buses are load buses.

At no-load condition a shunt inductive. Distance relays on D. C line inductor Q. Series capacitance on A. The reactance of the line connecting the generator to the motor is 0. Reactive power sources S. Then the values of Z The line to line voltage at the load terminals is measured to be less than 11 kV. The inductance and the capacitance of the cable are 0. The two ends of the feeder are fed by voltage sources such that VP. The line-to line voltage at the terminals of the machine is maintained constant at 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 A MVAR B The per unit positive-sequence. The per unit positive sequence impedance of the line based on MVA and 11 kV is j0. The magnitude of the voltage at the junction due to surge is A The inductance and capacitance of the overhead transmission lines are 1. A solid ground fault occurs at one phase of the far end of the transmission line.

Under frequency relay 2. The voltage of the alternator neutral with respect to ground during the fault is A Choose the correct match from the four choices given below: Alternators 6. Turbines R. Differential relay 3. Shunt capacitors 5. Minimum and maximum loads on each unit are 50 MW and MW respectively. The per unit positive-. Busbars S. The maximum power that could be delivered by the generator is 2. Buchholz relay 4. Transformers Q. All per unit values are based on the machine ratings.

A three-phase fault occurs at the terminals of the generator which reduces the generator output to zero. The original network is then restored. Distance relay 1. Transmission lines Codes: Assume that all the three units are operating all the time.

The fault is cleared after tc second. If the plant is operating on economic load dispatch to supply the total power demand of MW. The positive-sequence component of the load current is A 1. A generation of G2 and G3 is increased equally while generation of G1 is unchanged. D generally of G1. If the load of the system is increased.

If the input power factor is to be improved to 0. The Zone-1 and Zone-2 settings for both the relays are indicated on the diagram. Which of the following indicates the correct time setting for the Zone-2 of relays R1 and R2. C generation of G1. One generator G1 has a speed governor which maintains its speed constant at the rated value. The neutral of the alternator and the star point of the load are solidly grounded. B generation of G1 alone is increased while generation of G2 and G3 is unchanged.

G2 and G3 is increased in the ratio 0. The transmission losses are negligible. G2 and G3 is increased equally. The firing angle a as measured from the point of natural commutation is constrained to lie between 5c and 30c.

The parameters of the transmission line are as follows: The zero sequence impedance values expressed in pu on a common base and are indicated in figure. The Thevenin equivalent zero sequence impedance at point B is A 0. If the load flow program is run with this incomplete data A The load-flow will converge only if the slack bus is specified in area 1 B The load-flow will converge only if the slack bus is specified in area 2 nodia. Reactive power compensation is applied at the midpoint of the line and it is controlled such that the midpoint voltage of the transmission line is always maintained at 0.

While entering the network data. If the dc side current and ac side voltage magnitudes are constant. It is required to carry out a load-flow study on this system. If voltage at both ends of the line are maintained at 1. The equation describing the voltage drop in both lines is given below.

Z All quantities are expressed on a common base. The generator data is as follows: If at the instant of switch closure. Z in the following equations. The generator is initially running on open circuit with the frequency of the open circuit voltage slightly higher than that of the infinite bus. I 02 are the zero sequence voltage drops and currents for the two lines respectively.

If the capacitor supplies VAR. The initial rms current in the generator in per unit is A 7.Y21 and Y22 for the network shown are A 0. Delta-star distribution transformer resistance is 0. System response of the given circuit can be obtained as. Series RL circuit with unit step input is shown in following figure 1. The line current when operating at full load rated conditions will be A System is unstable with 2-poles on RH of s -plane.

The firing angle a as measured from the point of natural commutation is constrained to lie between 5c and 30c. Than Torque is decreased.