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tween its induced voltage and the bus bar voltage, so in the

parallel operation of compound generators the difference between

the induced voltage in a given machine and the bus bar voltage

determines the amount of current supplied by the machine. The

induced voltage in a shunt generator depends primarily on the

field strength and on the speed of the machine. In the compound

generator, however, the induced voltage depends not only on the

field strength produced by the shunt winding and on the speed,

6

66 LABORATORY MANUAL

but also on the additional field produced by the series winding.

Hence, the equal or proportionate sharing of the load with com-

pound generators depends on an additional factor, namely, the

strength of the field magnetism produced by the series field cur-

rent.

If two compound generators are connected in parallel (in gen-

eral as shown in Fig. 19, except that a series winding is inserted

between the upper armature terminal and the machine ammeter

in each case), each machine may be made to deliver its share of

a given total bus bar load by adjusting its shunt field rheostat.

If the machines are over-compounded, however, and one machine

speeds up due to an increase in the speed of its driving engine,

this means an increase in the induced voltage (due to the in-

crease in speed). The output of this machine is then increased

(meaning, of course, that the output of the second machine falls

off by a corresponding amount) and the action of the series wind-

ing is to increase still further the induced voltage in the first

machine. This condition being cumulative, results in an ex-

cessive overload for the first machine and obviously in an Unbal-

anced condition of operation. (This effect of instability is more

noticeable with over-compounded than with flat or under-com-

pounded generators.)

To prevent this unstable condition an equalizer connection is

made between the two machines, at the junction of the series

winding and the armature terminal in each case (for the short

shunt connection), and this places the two series windings in

parallel with each other as regards the output current from the

machines, thus insuring that the series field current will be in-

versely proportional to the resistance of the windings at all times,

irrespective of any tendency for the armature currents to be

unequal.

If the compounding of the machines is different, thus causing

an unequal sharing of a given total bus bar load, the resistance of

the series field circuit must be changed by connecting an auxili-

ary resistance in series with the series winding, thus reducing the

part of the total current which flows through the series winding

of the first machine and allowing more current to flow through

the series winding of the second machine.

Adjustments of the compounding by means of a shunt around

the series field, as explained in Experiment 11, will not serve the

DIRECT CURRENT 67

purpose in this case on account of the parallel condition of the

two series windings. (Note: The student should make a dia-

gram, similar to Fig. 19, on the data sheet with the series fields

arranged for the short shunt connection, and verify, theoretically,

the instability of operation without an equalizer connection. Al-

so, with an equalizer connection on the diagram, the statements

in the two preceding paragraphs should be verified before the

experiment is undertaken. )

Current Supply. From the Compound Generators assigned.

Apparatus Required. (1) Two compound generators (prefer-

ably over-compounded) ; (2) lamp banks to be used as a common

load supplied from the bus bars; (3) field rheostats for each ma-

chine; (4) a double-pole single-throw switch for each machine

and for the total load (3 in all) ; (5) ammeters, one for each ma-

chine, one for the total output current from the bus bars, and one

to be connected in the equalizer circuit between the two machines

(the latter instrument preferably a double-throw ammeter to in-

dicate the current no matter in which direction it flows) ; (6)

two voltmeters, one for the bus bars and one for the on-coming

machine; (7) equalizer connection (a wire to be connected be-

tween the two machines at the junction of the series field and the

armature in each case, where the short shunt connection is used ) .

Order of Work. 1. Arrange the connections of the two assigned

compound generators similar to Fig. 19, except that the series

field is to be connected between the upper armature terminal and

the ammeter in each case, and the equalizer is to be connected

between the upper armature terminals of the two machines

through an ammeter.

2. With all switches open, start the two generators and adjust

the voltage of each to its normal value.

3. Connect one of the generators ("A") to the bus bars (two

lengths of wire) and turn on enough lamps to load the machine

to its full capacity.

4. Adjust the voltage of the other generator ("B") to the

same value as the bus bar voltage (or a trifle lower) and connect

it to the bus bars, being sure that the positive terminal of the

machine is connected to the positive terminal of the bus bars.

(Remember that as soon as machine "B" is thrown on to the bus

bars, a current will flow through its series field from machine

68 LABORATORY MANUAL

11 A" which will tend to increase the induced voltage in the arma-

ture of "B". This is the reason for adjusting the voltage of

"B" a trifle lower than the bus bar voltage before connecting the

two. Watch the ammeter of machine "B" carefully until the ad-

justments of load have been made according to the following

item.)

5. Vary the shunt field rheostat of machine "B" until the cur-

rent of the two machines is the same in value, at the same time

adjusting the shunt field rheostat of machine "A" so that the

bus bar voltage remains constant. Then turn on enough lamps to

load each machine to its full rated capacity.

6. With both machines fully loaded, observe and record the

bus bar voltage, current delivered by each machine, total current

taken from the bus bars, and the equalizer current (noting in

which direction the equalizer current flows, that is, whether from

machine "A" to "B", or from "B" to "A".)

7. With the field rheostats untouched, repeat the observations

called for in item 6, for %, %, and a /4 of the total load, and for

zero current from the bus bars in turn.

8. Turn on the lamps and vary the field rheostats and lamps

until each machine delivers one-half of its rated load. Adjust

the field rheostat of the two machines until machine "B" is de-

livering all the current and machine "A" is unloaded, maintain-

ing constant voltage at the bus bars throughout the adjustment.

Now disconnect machine "A" from the bus bars.

9. Same as items 6 and 7, with a resistance inserted in one of

the series field circuits, so that when the load from the bus bars

equals the total rated capacity of the two machines combined,

machine "A" is delivering l 1 /^ of its rated capacity and machine

"B" % of its rated capacity.

Written Report. 1. Explain why the operation of compound

generators in parallel is unstable without an equalizer connec-

tion.

2. Why is this unstable condition less noticeable for flat and

under-compounded than for over-compounded machines ?

3. What current was indicated by the equalizer circuit am-

meter in items 5, 6 and 7, Order of Work? If any, to what was it

due?

DIRECT CURRENT 69

4. Explain any inequalities observed in the sharing of the

total bus bar load by the two machines, as the total output was

reduced in items 6, 7 and 9. If inequalities existed, to what were

they due? Explain.

5. Explain the use of resistance in series with one of the series

field windings in item 9. How did it affect the proportionate

sharing of the total output by the two machines as the total out-

put was reduced ?

6. Why cannot a shunt around the series field be used for the

purpose of adjusting the sharing of the total output in item 9 in-

stead of a resistance in series with the series field winding ? What

is the function of the resistance as here used? Explain.

Experiments 21 to 30, inclusive, constitute the

Alternating Current portion of the Manual.

ALTERNATING CURRENT

EXPERIMENT 21.

Resistance and Reactance in Series.

See Articles 261, 269, 270, 271, 272, 277, 278 and 279 in the

text book.

The object of this experiment is to make a study of the volt-

age, current and power relations in a simple alternating current

circuit containing both resistance and reactance in series.

Theory. Ohm's law states that in a circuit, or portion of a

complete circuit, where all the voltage goes to overcome resistance

only, the current (7) equals E/R, where E is the electromotive

force across the terminals of the circuit and R is the resistance of

the circuit in ohms. This law holds true for both direct and al-

ternating current circuits as regards that portion of E which

overcomes resistance (R) only.

In a direct current motor, the voltage (E) across the termi-

nals of the armature is partly used to overcome resistance and

partly to overcome the counter electromotive force induced in the

armature by the rotation of the armature wires in the magnetic

field, that is, E^ (the impressed electromotive force) =RI-\-E 2

(the counter electromotive force of the armature). Note that the

RI drop and E 2 are added numerically.

In an alternating current circuit consisting of a coil of wire,

the voltage (E r ) across the terminals of the coil is partly used to

overcome resistance and partly to overcome the counter electro-

motive force induced in the coil by the rapid reversals of the mag-

netic field in the coil due to the alternating current, that is, E^

(the impressed electromotive force) =RI added vectorially to E 2

(the counter electromotive force in the coil). Note that the RI

drop and E 2 are added vectorially (not numerically) because

they are 90 apart in phase. E 2 , the counter electromotive force,

is usually expressed as XI, that is, the reactance (X) of the cir-

71

72 LABOR A TORY MANUAL

cult times the current (7), X being the opposition due to the in-

ductance of the coil, but for convenience expressed in ohms like

the resistance R. (Read carefully Articles 165 and 171 in the

text book. )

Since the reactance of a circuit depends on the frequency of

the alternating electromotive force across its terminals, the oppo-

sition due to reactance is high for high frequencies and low for

low frequencies in a given circuit. Obviously the frequency has

nothing whatever to do with the RI drop in a circuit. Hence,

if an alternating current of 10 amperes flows in a circuit contain-

ing both R and X when 110 volts at 60 cycles are applied at its

terminals, if the frequency is reduced to 30 cycles, and the cur-

rent maintained at 10 amperes by reducing the electromotive

force, the RI component of E will, of course, remain the same,

while the XI component will be i/2 as great as before because X

is % its former value. A coil containing both resistance and re-

actance produces the same result as a separate resistance and a

separate reactance connected in series.

Since the voltage required to overcome R and X is made up of

two components 90 apart in phase, the combined effect of the

two (R and X) may be expressed as Z, which equals the square

root of (R 2 -{-X 2 ). Z (expressed in ohms) is usually termed the

impedance of the circuit, and it represents the total opposition

to the flow of current in an alternating current circuit due both

to resistance and to counter electromotive force (or reactance).

In a direct current circuit containing several resistances in

series when a current (/) flows, the volts drop across the vari-

ous resistances added together numerically determine the total

voltage of the circuit. Similarly, in an alternating current cir-

cuit, containing both resistance (R) and reactance (X) in series,

the volts drop across the various resistances and reactances are

added vectoriaUy to determine the total voltage of the circuit.

In the direct current circuit the power in the circuit equals

the electromotive force (E) times the current (7) because both

E and 7 may be thought of as in the same direction at all times.

In the alternating current circuit, the power in the circuit also

equals El in those cases where E and 7 are in the same direction

at all times (that is, in phase with each other), as in a circuit

containing resistance only. Where E and 7 are not in the same

direction at all times, (that is, out of phase) as in circuits con-

ALTERNATING CURRENT

73

taining reactance as well as resistance, account must be taken of

the fact that E and 7 are out of phase by an angle ''a", and the

product El must be multiplied by a factor called the power fac-

tor (cos a) of the circuit. A wattmeter, however, indicates the

true power (El cos a) at all times, even in those cases where the

voltmeter reading (E) and the ammeter reading (/) taken to-

gether do not indicate the true power.

Supply Mains

(110 Volts 60 Cycles A. C.)

A

r i r I

Voltmeter

C=?

"R" (Lamps in Parallel)

Adjustable Resistance

Fig. 19. Study of the voltage and current relations in series cir-

cuits, made up, in this case, of a reactance coil and a lamp bank in

series. The adjustable resistance shown to the left is an auxiliary to

the apparatus under test.

In a circuit like that of Fig. 19, where a coil, with both resist-

ance and reactance is connected in series with a resistance (lamp

bank), the current (7) is obviously the same throughout the cir-

cuit and the voltage E 3 across the entire circuit is equal to the RI

drop (EJ across the lamps added vectorially to the voltage (E 2 )

across the coil. The relation of these 3 voltages, each of which

may be measured separately by a voltmeter, is shown in Fig. 20.

This diagram also shows graphically how the reactance (X) of

the coil may be determined from the voltage readings.

Current Supply. 110 volts 50 and 60 cycle Alternating Cur-

rent and 110 volts Direct Current.

Apparatus Required. (1) Reactance coil; (2) circuit contain-

ing resistance only, for example, a lamp bank; (3) voltmeter

74 LABORATORY MANUAL

with rather large range; (4) voltmeter with low range (for meas-

uring the RI drop when Direct Current is used) ; (5) ammeter;

and (6) wattmeter.

Order of Work. 1. Connect the coil and the resistance (R) in

series as shown in Fig. 19 (the auxiliary resistance is put in to

permit of current adjustments). Adjust the auxiliary resist-

ance until a fair value of current flows from the 110-volt, 60-

cycle Alternating Current mains. Keeping this current constant.

(Resistance R) RI in Coil

a = Phase Difference Between ES and I

Fig. 20. Vector relations of the voltages and current in series cir-

cuits, as in Fig. 19.

observe and record the volts across the coil, across the resistance

(R), the total volts, not including the auxiliary resistance, cur-

rent, frequency, and total watts, not including the auxiliary re-

sistance. Use Form 12.

2. Connect the same coil and resistance (R) to the 110-volt

Direct Current mains, and reduce the voltage across the coil

and resistance (R) by the auxiliary resistance until the current

is the same value as in item 1. Observe and record the same

readings called for in item 1.

3. Same as item 1, except that R is to have'l 2/3, 1 1/3, 2/3

and then 1/3 the original value in turn, adjust to the same cur-

rent as in item 1 in each case, and repeat the observations called

for in item 1.

4. Connect the coil and the resistance (R) as in item 1 to 50

(or less) cycle Alternating Current mains and adjust the current

ALTERNATING CURRENT

75

until it is the same value as in items 1 and 2.

servations called for in item 1.

Take the same ob-

Written Report. 1. From the observations in item 1, Order of

Work, draw a diagram similar to Fig. 20, and from this deter-

mine graphically the reactance volts (XI) drop of the coil and

the phase difference between E s and I in degrees; also calculate

the reactance (X) in ohms and the power factor of the entire cir-

cuit not including the auxiliary resistance. The power factor=

watts (indicated by wattmeter) /EJ, that is, true watts divided

by apparent watts.

No.

Supply

Current

Volts

Amperes

Frequency

Watts

(Total)

"R"

Coil

Total

1

(A. C.)

2

(D. C.)

3

(A. C.)

Form 12.

2. Is E Z I in item 2, Order of Work, the same in value as the

wattmeter reading in item 1, Order of Work, for the same value

of current (/) in each case? If so, why? If not, why?

3. Draw a vector diagram, similar to Fig. 20, for the voltages

observed in items 3 and 4, Order of Work, and repeat the require-

ments under 1, Written Report.

4. How do the reactance volts drop in items 1 and 4, Order of

Work, compare?

(Note: The impedance of an alternating current circuit often

involves reactance due to capacity as well as to inductance, but

for simplicity this experiment has been limited to the effect due

to resistance and inductive reactance only.)

76

LABORATORY MANUAL

EXPERIMENT 22.

Resistance and Reactance in Parallel.

See Article 273 in the text book, also the Theory under Ex-

periment 21 in the Manual.

The object of this experiment is to make a study of the volt-

age, current and power relations in a simple alternating current

circuit containing both resistance and reactance in parallel.

Supply Mains

(110 Volts 60 Cycles A C.)

r nb

Fig. 21. Study of the current and voltage relations in parallel cir-

cuits, made up, in this case, of a reactance coil and a lamp bank. Note

that the two ammeters to the right measure the current in the coil and

in the lamp bank, respectively.

Theory. In direct current circuits where a number of resist-

ances are connected in series, the current is the same throughout

the circuit, while the volts drop across the separate resistances

are added numerically to determine the total voltage of the cir-

cuit. In the alternating current circuit, where resistances and

reactances are connected in series the current is also obviously

the same throughout the circuit, while the volts drop across the

various parts of the circuit are added vectorially to determine

ALTERNATING CURRENT 77

the total voltage. These have been investigated in experiment

21.

In direct current circuits where a number of resistances are

connected in parallel, the voltage is obviously the same across

each of the resistances, while the total current is equal to the

numerical sum of the individual currents in the various resist-

ances. In the alternating current circuit, where resistances and

reactances are connected in parallel, the voltage is the same

across the terminals of each portion of the circuit, while the total

current is equal to the vector sum of the individual currents

through the separate parts of the circuit.

a = Phase Difference Between E and Is

Fig. 22. Vector relations of the currents and voltage in parallel cir-

cuits, as in Pig. 21.

In a circuit like that of Fig. 21, where a coil with both resist-

ance and reactance is connected in parallel with a resistance

(lamp bank), the voltage (E) is the same for both parts of the

circuit, and the total current (7 3 ) is equal to the current 7 2 in the

coil added veetorially to the current 7 X in the lamp bank. The

diagram shown in Fig. 22 indicates the relations of these three cur-

rents, each of which may be measured separately by an ammeter.

From this diagram the phase difference between 7 X , 7 2 and 7 3 may

be determined graphically.

Current Supply. 110 volts 50 and 60 cycle Alternating Cur-

rent and 110 volts Direct Current.

78 LABORATORY MANUAL

Apparatus Required. (1) Reactance coil; (2) circuit contain-

ing resistance only (lamp bank) ; (3) ammeters, one for each cir-

cuit and one for the total current; (4) voltmeter; and (5) watt-

meter.

Order of Work. 1. Connect the coil and the lamp bank in par-

allel to the 60-cycle mains, as shown in Fig. 21, with due care

that the current through the coil is not excessive. Observe and

record the current in the coil, in the lamp bank and the total

current, volts, frequency and total watts.

2. Connect the coil and lamp bank to the 110-volt Direct Cur-

rent mains, adjusting the voltage if necessary to the same value

as used in item 1. Observe and record the same readings called

for in item 1. (Note: If the current through the coil is exces-

sive with the Direct Current, insert a protective resistance in

series with it to bring down the current to a normal value, and

repeat item 1 with this extra resistance in circuit so as to have

the voltage conditions the same in both items 1 and 2.)

3. Same as item 1, except that R is to have 1 1/3 and 2/3 the

original value in turn, use the same voltage as in item 1 in each

case, and repeat the observations called for in item 1.

4. Same as item 1, except that a reactance coil with a different

power factor from the original coil is to be substituted for the

lamp bank. Use the same voltage as in item 1, and repeat the ob-

servations called for in item 1.

5. Connect the coil and the lamp bank to the 50-cycle mains,

and adjust the voltage to the same value as in items 1 and 2.

Take the same observations called for in item 1.

Written Report. 1. From the observations in item 1, Order of

Work, draw a diagram similar to Fig. 22, and from this deter-

mine graphically the phase difference between E and 7 3 in de-

grees and calculate the power factor of the entire circuit (true

watts divided by apparent watts).

2. Does EI^ (Direct Current) equal EI^ (Alternating Cur-

rent) in items 1 and 2, Order of Work? If so, why? If not,

why?

3. Same as item 1, Written Report, for items 3 and 4, Order

of Work.

ALTERNATING CURRENT 79

4. Draw a vector diagram similar to Fig. 22 for the current

values observed in item 5, Order of Work, and repeat the require-

ments called for under item 1, Written Report.

5. How do the current values through the coil compare in items

1, 3 and 5, Order of Work?

6. Does EI. A in item 2, Order of Work, equal the wattmeter

reading in item 1, Order of Work? If so, why ? If not, why?

(Note: The impedance of an alternating current circuit often

involves reactance due to capacity as well as to inductance, but

for simplicity this experiment has been limited to the effect due

to resistance and inductive reactance only.)

EXPERIMENT 23.

Study of Three-Phase Circuits.

See Article 282 in the text book.

The object of this experiment is to afford an opportunity for

observing the voltage and current relations in three-phase cir-

cuits. (Note: Two-phase circuits are somewhat simpler and the

relations between phases perhaps more readily understood, hence,

where the laboratory apparatus is two-phase, the following ex-

periment may be carried out with the two-phase instead of the

three-phase apparatus as here suggested.)

Theory. As three-phase alternating current transmission of

electric power is very generally used over long distances, and

further, since many three-phase induction motors are in service,

the general relations of voltage and current in such circuits are

of special interest.

A single winding on the armature of an alternating current

generator with two collector rings for delivering the current, is

called a single-phase machine. Two electrically separate wind-

ings may be used instead of one, each winding terminating in a

set of two collector rings and thus making a two-phase machine.

The two windings in such a case are wound with a definite angu-

lar displacement between corresponding wires, this displacement

being such that the electromotive forces in the two coils differ

by 90 in phase. Similarly, three electrically separate coils may

be wound on the armature for making a three-phase generator,

80

LABORATORY MANUAL

the displacement of the wires of the three windings being such

that the electromotive forces differ in phase by 120 from each

other.

The principal advantages of the three-phase as compared with

the single-phase current are first, the economy in the amount of

copper wire required for the transmission of a given amount of

power by the three-phase scheme, and second, the improved con-

Fig. 23. Study of the voltage and current relations in a three-phase

"Y" (or Star) connected receiving circuit.

ditions afforded by three-phase currents in the operation of in-

duction motors, and other apparatus.

parallel operation of compound generators the difference between

the induced voltage in a given machine and the bus bar voltage

determines the amount of current supplied by the machine. The

induced voltage in a shunt generator depends primarily on the

field strength and on the speed of the machine. In the compound

generator, however, the induced voltage depends not only on the

field strength produced by the shunt winding and on the speed,

6

66 LABORATORY MANUAL

but also on the additional field produced by the series winding.

Hence, the equal or proportionate sharing of the load with com-

pound generators depends on an additional factor, namely, the

strength of the field magnetism produced by the series field cur-

rent.

If two compound generators are connected in parallel (in gen-

eral as shown in Fig. 19, except that a series winding is inserted

between the upper armature terminal and the machine ammeter

in each case), each machine may be made to deliver its share of

a given total bus bar load by adjusting its shunt field rheostat.

If the machines are over-compounded, however, and one machine

speeds up due to an increase in the speed of its driving engine,

this means an increase in the induced voltage (due to the in-

crease in speed). The output of this machine is then increased

(meaning, of course, that the output of the second machine falls

off by a corresponding amount) and the action of the series wind-

ing is to increase still further the induced voltage in the first

machine. This condition being cumulative, results in an ex-

cessive overload for the first machine and obviously in an Unbal-

anced condition of operation. (This effect of instability is more

noticeable with over-compounded than with flat or under-com-

pounded generators.)

To prevent this unstable condition an equalizer connection is

made between the two machines, at the junction of the series

winding and the armature terminal in each case (for the short

shunt connection), and this places the two series windings in

parallel with each other as regards the output current from the

machines, thus insuring that the series field current will be in-

versely proportional to the resistance of the windings at all times,

irrespective of any tendency for the armature currents to be

unequal.

If the compounding of the machines is different, thus causing

an unequal sharing of a given total bus bar load, the resistance of

the series field circuit must be changed by connecting an auxili-

ary resistance in series with the series winding, thus reducing the

part of the total current which flows through the series winding

of the first machine and allowing more current to flow through

the series winding of the second machine.

Adjustments of the compounding by means of a shunt around

the series field, as explained in Experiment 11, will not serve the

DIRECT CURRENT 67

purpose in this case on account of the parallel condition of the

two series windings. (Note: The student should make a dia-

gram, similar to Fig. 19, on the data sheet with the series fields

arranged for the short shunt connection, and verify, theoretically,

the instability of operation without an equalizer connection. Al-

so, with an equalizer connection on the diagram, the statements

in the two preceding paragraphs should be verified before the

experiment is undertaken. )

Current Supply. From the Compound Generators assigned.

Apparatus Required. (1) Two compound generators (prefer-

ably over-compounded) ; (2) lamp banks to be used as a common

load supplied from the bus bars; (3) field rheostats for each ma-

chine; (4) a double-pole single-throw switch for each machine

and for the total load (3 in all) ; (5) ammeters, one for each ma-

chine, one for the total output current from the bus bars, and one

to be connected in the equalizer circuit between the two machines

(the latter instrument preferably a double-throw ammeter to in-

dicate the current no matter in which direction it flows) ; (6)

two voltmeters, one for the bus bars and one for the on-coming

machine; (7) equalizer connection (a wire to be connected be-

tween the two machines at the junction of the series field and the

armature in each case, where the short shunt connection is used ) .

Order of Work. 1. Arrange the connections of the two assigned

compound generators similar to Fig. 19, except that the series

field is to be connected between the upper armature terminal and

the ammeter in each case, and the equalizer is to be connected

between the upper armature terminals of the two machines

through an ammeter.

2. With all switches open, start the two generators and adjust

the voltage of each to its normal value.

3. Connect one of the generators ("A") to the bus bars (two

lengths of wire) and turn on enough lamps to load the machine

to its full capacity.

4. Adjust the voltage of the other generator ("B") to the

same value as the bus bar voltage (or a trifle lower) and connect

it to the bus bars, being sure that the positive terminal of the

machine is connected to the positive terminal of the bus bars.

(Remember that as soon as machine "B" is thrown on to the bus

bars, a current will flow through its series field from machine

68 LABORATORY MANUAL

11 A" which will tend to increase the induced voltage in the arma-

ture of "B". This is the reason for adjusting the voltage of

"B" a trifle lower than the bus bar voltage before connecting the

two. Watch the ammeter of machine "B" carefully until the ad-

justments of load have been made according to the following

item.)

5. Vary the shunt field rheostat of machine "B" until the cur-

rent of the two machines is the same in value, at the same time

adjusting the shunt field rheostat of machine "A" so that the

bus bar voltage remains constant. Then turn on enough lamps to

load each machine to its full rated capacity.

6. With both machines fully loaded, observe and record the

bus bar voltage, current delivered by each machine, total current

taken from the bus bars, and the equalizer current (noting in

which direction the equalizer current flows, that is, whether from

machine "A" to "B", or from "B" to "A".)

7. With the field rheostats untouched, repeat the observations

called for in item 6, for %, %, and a /4 of the total load, and for

zero current from the bus bars in turn.

8. Turn on the lamps and vary the field rheostats and lamps

until each machine delivers one-half of its rated load. Adjust

the field rheostat of the two machines until machine "B" is de-

livering all the current and machine "A" is unloaded, maintain-

ing constant voltage at the bus bars throughout the adjustment.

Now disconnect machine "A" from the bus bars.

9. Same as items 6 and 7, with a resistance inserted in one of

the series field circuits, so that when the load from the bus bars

equals the total rated capacity of the two machines combined,

machine "A" is delivering l 1 /^ of its rated capacity and machine

"B" % of its rated capacity.

Written Report. 1. Explain why the operation of compound

generators in parallel is unstable without an equalizer connec-

tion.

2. Why is this unstable condition less noticeable for flat and

under-compounded than for over-compounded machines ?

3. What current was indicated by the equalizer circuit am-

meter in items 5, 6 and 7, Order of Work? If any, to what was it

due?

DIRECT CURRENT 69

4. Explain any inequalities observed in the sharing of the

total bus bar load by the two machines, as the total output was

reduced in items 6, 7 and 9. If inequalities existed, to what were

they due? Explain.

5. Explain the use of resistance in series with one of the series

field windings in item 9. How did it affect the proportionate

sharing of the total output by the two machines as the total out-

put was reduced ?

6. Why cannot a shunt around the series field be used for the

purpose of adjusting the sharing of the total output in item 9 in-

stead of a resistance in series with the series field winding ? What

is the function of the resistance as here used? Explain.

Experiments 21 to 30, inclusive, constitute the

Alternating Current portion of the Manual.

ALTERNATING CURRENT

EXPERIMENT 21.

Resistance and Reactance in Series.

See Articles 261, 269, 270, 271, 272, 277, 278 and 279 in the

text book.

The object of this experiment is to make a study of the volt-

age, current and power relations in a simple alternating current

circuit containing both resistance and reactance in series.

Theory. Ohm's law states that in a circuit, or portion of a

complete circuit, where all the voltage goes to overcome resistance

only, the current (7) equals E/R, where E is the electromotive

force across the terminals of the circuit and R is the resistance of

the circuit in ohms. This law holds true for both direct and al-

ternating current circuits as regards that portion of E which

overcomes resistance (R) only.

In a direct current motor, the voltage (E) across the termi-

nals of the armature is partly used to overcome resistance and

partly to overcome the counter electromotive force induced in the

armature by the rotation of the armature wires in the magnetic

field, that is, E^ (the impressed electromotive force) =RI-\-E 2

(the counter electromotive force of the armature). Note that the

RI drop and E 2 are added numerically.

In an alternating current circuit consisting of a coil of wire,

the voltage (E r ) across the terminals of the coil is partly used to

overcome resistance and partly to overcome the counter electro-

motive force induced in the coil by the rapid reversals of the mag-

netic field in the coil due to the alternating current, that is, E^

(the impressed electromotive force) =RI added vectorially to E 2

(the counter electromotive force in the coil). Note that the RI

drop and E 2 are added vectorially (not numerically) because

they are 90 apart in phase. E 2 , the counter electromotive force,

is usually expressed as XI, that is, the reactance (X) of the cir-

71

72 LABOR A TORY MANUAL

cult times the current (7), X being the opposition due to the in-

ductance of the coil, but for convenience expressed in ohms like

the resistance R. (Read carefully Articles 165 and 171 in the

text book. )

Since the reactance of a circuit depends on the frequency of

the alternating electromotive force across its terminals, the oppo-

sition due to reactance is high for high frequencies and low for

low frequencies in a given circuit. Obviously the frequency has

nothing whatever to do with the RI drop in a circuit. Hence,

if an alternating current of 10 amperes flows in a circuit contain-

ing both R and X when 110 volts at 60 cycles are applied at its

terminals, if the frequency is reduced to 30 cycles, and the cur-

rent maintained at 10 amperes by reducing the electromotive

force, the RI component of E will, of course, remain the same,

while the XI component will be i/2 as great as before because X

is % its former value. A coil containing both resistance and re-

actance produces the same result as a separate resistance and a

separate reactance connected in series.

Since the voltage required to overcome R and X is made up of

two components 90 apart in phase, the combined effect of the

two (R and X) may be expressed as Z, which equals the square

root of (R 2 -{-X 2 ). Z (expressed in ohms) is usually termed the

impedance of the circuit, and it represents the total opposition

to the flow of current in an alternating current circuit due both

to resistance and to counter electromotive force (or reactance).

In a direct current circuit containing several resistances in

series when a current (/) flows, the volts drop across the vari-

ous resistances added together numerically determine the total

voltage of the circuit. Similarly, in an alternating current cir-

cuit, containing both resistance (R) and reactance (X) in series,

the volts drop across the various resistances and reactances are

added vectoriaUy to determine the total voltage of the circuit.

In the direct current circuit the power in the circuit equals

the electromotive force (E) times the current (7) because both

E and 7 may be thought of as in the same direction at all times.

In the alternating current circuit, the power in the circuit also

equals El in those cases where E and 7 are in the same direction

at all times (that is, in phase with each other), as in a circuit

containing resistance only. Where E and 7 are not in the same

direction at all times, (that is, out of phase) as in circuits con-

ALTERNATING CURRENT

73

taining reactance as well as resistance, account must be taken of

the fact that E and 7 are out of phase by an angle ''a", and the

product El must be multiplied by a factor called the power fac-

tor (cos a) of the circuit. A wattmeter, however, indicates the

true power (El cos a) at all times, even in those cases where the

voltmeter reading (E) and the ammeter reading (/) taken to-

gether do not indicate the true power.

Supply Mains

(110 Volts 60 Cycles A. C.)

A

r i r I

Voltmeter

C=?

"R" (Lamps in Parallel)

Adjustable Resistance

Fig. 19. Study of the voltage and current relations in series cir-

cuits, made up, in this case, of a reactance coil and a lamp bank in

series. The adjustable resistance shown to the left is an auxiliary to

the apparatus under test.

In a circuit like that of Fig. 19, where a coil, with both resist-

ance and reactance is connected in series with a resistance (lamp

bank), the current (7) is obviously the same throughout the cir-

cuit and the voltage E 3 across the entire circuit is equal to the RI

drop (EJ across the lamps added vectorially to the voltage (E 2 )

across the coil. The relation of these 3 voltages, each of which

may be measured separately by a voltmeter, is shown in Fig. 20.

This diagram also shows graphically how the reactance (X) of

the coil may be determined from the voltage readings.

Current Supply. 110 volts 50 and 60 cycle Alternating Cur-

rent and 110 volts Direct Current.

Apparatus Required. (1) Reactance coil; (2) circuit contain-

ing resistance only, for example, a lamp bank; (3) voltmeter

74 LABORATORY MANUAL

with rather large range; (4) voltmeter with low range (for meas-

uring the RI drop when Direct Current is used) ; (5) ammeter;

and (6) wattmeter.

Order of Work. 1. Connect the coil and the resistance (R) in

series as shown in Fig. 19 (the auxiliary resistance is put in to

permit of current adjustments). Adjust the auxiliary resist-

ance until a fair value of current flows from the 110-volt, 60-

cycle Alternating Current mains. Keeping this current constant.

(Resistance R) RI in Coil

a = Phase Difference Between ES and I

Fig. 20. Vector relations of the voltages and current in series cir-

cuits, as in Fig. 19.

observe and record the volts across the coil, across the resistance

(R), the total volts, not including the auxiliary resistance, cur-

rent, frequency, and total watts, not including the auxiliary re-

sistance. Use Form 12.

2. Connect the same coil and resistance (R) to the 110-volt

Direct Current mains, and reduce the voltage across the coil

and resistance (R) by the auxiliary resistance until the current

is the same value as in item 1. Observe and record the same

readings called for in item 1.

3. Same as item 1, except that R is to have'l 2/3, 1 1/3, 2/3

and then 1/3 the original value in turn, adjust to the same cur-

rent as in item 1 in each case, and repeat the observations called

for in item 1.

4. Connect the coil and the resistance (R) as in item 1 to 50

(or less) cycle Alternating Current mains and adjust the current

ALTERNATING CURRENT

75

until it is the same value as in items 1 and 2.

servations called for in item 1.

Take the same ob-

Written Report. 1. From the observations in item 1, Order of

Work, draw a diagram similar to Fig. 20, and from this deter-

mine graphically the reactance volts (XI) drop of the coil and

the phase difference between E s and I in degrees; also calculate

the reactance (X) in ohms and the power factor of the entire cir-

cuit not including the auxiliary resistance. The power factor=

watts (indicated by wattmeter) /EJ, that is, true watts divided

by apparent watts.

No.

Supply

Current

Volts

Amperes

Frequency

Watts

(Total)

"R"

Coil

Total

1

(A. C.)

2

(D. C.)

3

(A. C.)

Form 12.

2. Is E Z I in item 2, Order of Work, the same in value as the

wattmeter reading in item 1, Order of Work, for the same value

of current (/) in each case? If so, why? If not, why?

3. Draw a vector diagram, similar to Fig. 20, for the voltages

observed in items 3 and 4, Order of Work, and repeat the require-

ments under 1, Written Report.

4. How do the reactance volts drop in items 1 and 4, Order of

Work, compare?

(Note: The impedance of an alternating current circuit often

involves reactance due to capacity as well as to inductance, but

for simplicity this experiment has been limited to the effect due

to resistance and inductive reactance only.)

76

LABORATORY MANUAL

EXPERIMENT 22.

Resistance and Reactance in Parallel.

See Article 273 in the text book, also the Theory under Ex-

periment 21 in the Manual.

The object of this experiment is to make a study of the volt-

age, current and power relations in a simple alternating current

circuit containing both resistance and reactance in parallel.

Supply Mains

(110 Volts 60 Cycles A C.)

r nb

Fig. 21. Study of the current and voltage relations in parallel cir-

cuits, made up, in this case, of a reactance coil and a lamp bank. Note

that the two ammeters to the right measure the current in the coil and

in the lamp bank, respectively.

Theory. In direct current circuits where a number of resist-

ances are connected in series, the current is the same throughout

the circuit, while the volts drop across the separate resistances

are added numerically to determine the total voltage of the cir-

cuit. In the alternating current circuit, where resistances and

reactances are connected in series the current is also obviously

the same throughout the circuit, while the volts drop across the

various parts of the circuit are added vectorially to determine

ALTERNATING CURRENT 77

the total voltage. These have been investigated in experiment

21.

In direct current circuits where a number of resistances are

connected in parallel, the voltage is obviously the same across

each of the resistances, while the total current is equal to the

numerical sum of the individual currents in the various resist-

ances. In the alternating current circuit, where resistances and

reactances are connected in parallel, the voltage is the same

across the terminals of each portion of the circuit, while the total

current is equal to the vector sum of the individual currents

through the separate parts of the circuit.

a = Phase Difference Between E and Is

Fig. 22. Vector relations of the currents and voltage in parallel cir-

cuits, as in Pig. 21.

In a circuit like that of Fig. 21, where a coil with both resist-

ance and reactance is connected in parallel with a resistance

(lamp bank), the voltage (E) is the same for both parts of the

circuit, and the total current (7 3 ) is equal to the current 7 2 in the

coil added veetorially to the current 7 X in the lamp bank. The

diagram shown in Fig. 22 indicates the relations of these three cur-

rents, each of which may be measured separately by an ammeter.

From this diagram the phase difference between 7 X , 7 2 and 7 3 may

be determined graphically.

Current Supply. 110 volts 50 and 60 cycle Alternating Cur-

rent and 110 volts Direct Current.

78 LABORATORY MANUAL

Apparatus Required. (1) Reactance coil; (2) circuit contain-

ing resistance only (lamp bank) ; (3) ammeters, one for each cir-

cuit and one for the total current; (4) voltmeter; and (5) watt-

meter.

Order of Work. 1. Connect the coil and the lamp bank in par-

allel to the 60-cycle mains, as shown in Fig. 21, with due care

that the current through the coil is not excessive. Observe and

record the current in the coil, in the lamp bank and the total

current, volts, frequency and total watts.

2. Connect the coil and lamp bank to the 110-volt Direct Cur-

rent mains, adjusting the voltage if necessary to the same value

as used in item 1. Observe and record the same readings called

for in item 1. (Note: If the current through the coil is exces-

sive with the Direct Current, insert a protective resistance in

series with it to bring down the current to a normal value, and

repeat item 1 with this extra resistance in circuit so as to have

the voltage conditions the same in both items 1 and 2.)

3. Same as item 1, except that R is to have 1 1/3 and 2/3 the

original value in turn, use the same voltage as in item 1 in each

case, and repeat the observations called for in item 1.

4. Same as item 1, except that a reactance coil with a different

power factor from the original coil is to be substituted for the

lamp bank. Use the same voltage as in item 1, and repeat the ob-

servations called for in item 1.

5. Connect the coil and the lamp bank to the 50-cycle mains,

and adjust the voltage to the same value as in items 1 and 2.

Take the same observations called for in item 1.

Written Report. 1. From the observations in item 1, Order of

Work, draw a diagram similar to Fig. 22, and from this deter-

mine graphically the phase difference between E and 7 3 in de-

grees and calculate the power factor of the entire circuit (true

watts divided by apparent watts).

2. Does EI^ (Direct Current) equal EI^ (Alternating Cur-

rent) in items 1 and 2, Order of Work? If so, why? If not,

why?

3. Same as item 1, Written Report, for items 3 and 4, Order

of Work.

ALTERNATING CURRENT 79

4. Draw a vector diagram similar to Fig. 22 for the current

values observed in item 5, Order of Work, and repeat the require-

ments called for under item 1, Written Report.

5. How do the current values through the coil compare in items

1, 3 and 5, Order of Work?

6. Does EI. A in item 2, Order of Work, equal the wattmeter

reading in item 1, Order of Work? If so, why ? If not, why?

(Note: The impedance of an alternating current circuit often

involves reactance due to capacity as well as to inductance, but

for simplicity this experiment has been limited to the effect due

to resistance and inductive reactance only.)

EXPERIMENT 23.

Study of Three-Phase Circuits.

See Article 282 in the text book.

The object of this experiment is to afford an opportunity for

observing the voltage and current relations in three-phase cir-

cuits. (Note: Two-phase circuits are somewhat simpler and the

relations between phases perhaps more readily understood, hence,

where the laboratory apparatus is two-phase, the following ex-

periment may be carried out with the two-phase instead of the

three-phase apparatus as here suggested.)

Theory. As three-phase alternating current transmission of

electric power is very generally used over long distances, and

further, since many three-phase induction motors are in service,

the general relations of voltage and current in such circuits are

of special interest.

A single winding on the armature of an alternating current

generator with two collector rings for delivering the current, is

called a single-phase machine. Two electrically separate wind-

ings may be used instead of one, each winding terminating in a

set of two collector rings and thus making a two-phase machine.

The two windings in such a case are wound with a definite angu-

lar displacement between corresponding wires, this displacement

being such that the electromotive forces in the two coils differ

by 90 in phase. Similarly, three electrically separate coils may

be wound on the armature for making a three-phase generator,

80

LABORATORY MANUAL

the displacement of the wires of the three windings being such

that the electromotive forces differ in phase by 120 from each

other.

The principal advantages of the three-phase as compared with

the single-phase current are first, the economy in the amount of

copper wire required for the transmission of a given amount of

power by the three-phase scheme, and second, the improved con-

Fig. 23. Study of the voltage and current relations in a three-phase

"Y" (or Star) connected receiving circuit.

ditions afforded by three-phase currents in the operation of in-

duction motors, and other apparatus.

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