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Table of Contents. • U.S. Government Printing Office; 1945 - 618779
Chapter 7: Electrical
Power - Force
Scientists and technicians make a point of specifically defining all the terms they
use. They like their language to say exactly what they mean. This is necessary because
scientists use technical terms in explaining their work. With a good working knowledge
of such terms as force, power, work, emf, current, and resistance, you'll be far more
savvy about your own work. Too, you'll want to be sure so that you can shoot the breeze
about your job. Knowing exactly WHAT certain words MEAN helps a lot!
You often HEAR the word FORCE. But you USE force far. more) often than you hear the
word. Every time you lift something, you use force. Every time you move, you have exerted
force. A ship moves through the water because of force. In fact, every time anything
moves or tends to move, force has been exerted. Force may be a push or a pull. FORCE
then, IS THAT WHICH PRODUCES MOTION OR TENDS TO PRODUCE MOTION. Consider the force of
GRAVITY. It causes bodies to move toward the earth. Suppose you put a box on a table.
The box tends to move DOWNWARD because of gravity but the table exerts an UPWARD force
- the two forces are balanced. However, if the box is "too heavy" for the table, the
table cannot exert enough upward force to balance the pull of gravity and the table collapses.
The force exerted by a propeller is a MECHANICAL force. The explosion of hydrogen
and oxygen to form water is a CHEMICAL force. The force which causes electrons to flow
is an ELECTROMOTIVE force and its unit is the VOLT. There are many kinds of force, but
they ALL produce or tend to produce motion.
WORK IS A FORCE ACTING THROUGH SPACE. Imagine that you push with. all your strength
against a steel bulkhead. You probably think you've <;lone, work but technically you
HAVEN'T. True, you have exerted force on the bulkhead, but since the bulkhead hasn't
moved, NO WORK has been done. Now imagine that you exert the same force lifting a 200-pound
shell from the deck to a shelf 4 feet high. WORK HAS BEEN DONE, because the force acted
through space'. You exerted a 200pound FORCE through a DISTANCE of 4 feet.
Work = force x distance
so in this case -
Work =200 pounds x 4 feet = 800 foot-pounds (ft.-lb.)
NOTE that work and force are different. Force is exerted whenever a body is pushed
or pulled BUT work is done only IF THE BODY MOVES. In electricity, the unit of work is
ELECTRICAL WORK = VOLTAGE x COULOMBS = JOULES
The JOULE, by itself, has relatively little use because it does not take into consideration
the factor of TIME. That is, it might take 2 seconds or 2 days for 120 volts to move
1 coulomb (6.3 billion billions electrons); and in either case, you would have done 120
x 1 = 120 joules of electrical work. So time is really important - and that brings you
POWER IS THE TIME RATE OF DOING WORK. This relation is expressed -
Power = Work/Time
You have learned that the amount of WORK done has nothing to do with the time it takes
to do the work. BUT the amount of POWER depends on HOW FAST that work can be done. You
know that a steam shovel has a great deal more POWER than a man. Both can do the same
amount of work but the steam shovel will do it a lot FASTER. For example, say that 1,000
pounds of earth must be raised 20 feet. The work is -
Work = force x distance = 1,000 x 20 = 20,000 foot-pounds.
The steam shovel does the job in one scoop, taking 2 seconds. The man does the job
in 20 minutes (or 1,200 seconds). The steam shovel has -
Power = Work/Time = 20,000/2 = 10,000 ft-lb. per second
The man has -
Power = Work/Time = 20,000/1,200 = 16.7 ft-lb. per second
The steam shovel has exerted approximately 600 times as much POWER as the man even
though the WORK done by both is equal.
The mechanical unit of power - FOOT-POUNDS PER SECOND - is too small for practical
use. In the early days, power was generally supplied by horses, and experiments indicated
that an average horse could do 550 foot-pounds of work per second. This led to the establishment
of a larger unit-the HORSEPOWER (hp).
HP = 550 FT.-LBS. PER SECOND
What was the HP of the steam shovel in the preceding example?
10,000 ft.lbs. per sec./550 ft.lbs. per second = 18.2 hp
What was the HP of the man?
16.7 ft.-lbs. per second/550 ft.-lbs. per second - 0.032
Power in the electrical system is measured in WATTS.
Power = Work/Time = Volts x Coulombs/Time = Watts (w.)
Do you recognize the expression - Coulombs/Time? In Chapter 3, you learned that coulombs
divided by time was the time rate of flow of current - the AMPERE. So you can substitute
AMPERE for Coulomb/Time in the above equation, and the equation becomes -
Power = volts X amperes = Watts, or -
P=E x I
POWER IS AN IMPORTANT MEASURE IN ELECTRICITY. It tells you how much you can expect
from a motor or generator.
Study the circuit in figure 34. It shows a motor connected to its generator; and meters
are installed to read the values of current and voltage in the circuit. By multiplying
the ammeter and volt-meter readings, you get the power consumed by the motor -
P = E x I = 120 x 8 = 960 watts
which means that this motor CONSUMES 960 watts of power.
By measuring the amount of mechanical work a number of electric motors did in one
second, it was determined that- 746 Watts = 1 hp
Figure 34. - Power consumption of a motor.
Does the motor DELIVER 960 watts, or 960/746 = 1.29 hp, of power? No, because some
of the power is lost within the motor. This loss is caused by internal heat and friction.
All machines lose some power by heat and friction. If they didn't, they would be 100
percent EFFICIENT and there would be perpetual motion. EFFICIENCY is the percentage of
the total input power that is actually delivered as output. Motors deliver their power
at their shafts. Say that this particular motor is a one-hp job. This means that the
motor DELIVERS one hp AT ITS SHAFT.
What is its efficiency?
INPUT = 960 watts
OUTPUT = 1 hp = 746 watts
EFFICIENCY = Output/Input
= 746/960 = 0.777, or 77.7%
The motor is 77.7 percent efficient - in other words, it delivers 77.7 percent of
the power it consumes. The balance of power - 22.3 percent is lost as heat and friction.
Look at figure 35. It shows the power and the power losses as a picture. If you follow
the arrows through this picture of a motor, you will find the input power is ELECTRICAL
POWER. It splits up in the motor, going in two directions. The losses in the form of
heat are radiated upward, and the output in the form of MECHANICAL POWER is delivered
by a rotating shaft. This gives you the definition of a motor - A MACHINE WHICH CONVERTS
ELECTRICAL ENERGY INTO MECHANICAL ENERGY. (Just the opposite to the action of a generator.)
Figure 35. - Delivered and lost power in a motor.
How much work is this motor capable of doing? Since 1 hp = 550 ft-lbs. per second,
the motor can exert a force of 550 pounds through 1 foot of space every second. Or, 275
pounds through 2 feet of space every second. Or, 55 pounds through 10 feet of space every
second. You'll notice that the force decreases as the speed increases.
To be sure you understand these terms, consider a harder example. Figure 36 shows
a circuit involving a 10 hp motor, a generator, meters, and a 'l,000-foot length of double
wire connecting lines.
Figure 36. - Power loss in a long line.
The generator furnishes 440 volts of emf, but the motor draws 25 amperes at only 390
volts. The difference -50 volts - is used in pushing the current through the 2,000 feet
(1,000 ft. for each wire) of connecting wire.
You can calculate the resistance of this wire -
R = E/I = 50/25 = 2 Ω
which means that 50 volts of force are used in pushing 25 amperes of current through
2,000 feet of wire having 2 ohms of resistance.
How much power is consumed by the motor?
P = E x I = 390 x 25 = 9,750 w
What is the efficiency of this 10 hp motor?
Efficiency = output/input = 10 x 746/9.750 = 7.460/9,750
How much power is lost in the motor by heat and friction?
Losses = input - output = 9,750 - 7,460 = 2,290 w.
What is the power consumed by the line in delivering current to the motor?
P = E x I = 50 x 25 = 1,250 w.
As a check, you know that total power furnished, minus all losses, should give the
power output of the motor. In this case, 440 x 25 = 11,000 watts is the power furnished.
The losses are 2,290 + 1,250 = 3,540 watts. The output then is 11,000 - 3,540 = 7,460
watts. This checks with the rated output.
Remember - whenever work must be done, power is consumed doing it. It requires work
to force current through a wire - in this case, 1,250 watts of power is consumed by the
wire. It requires work to overcome the friction of the motor and force current through
its windings - 2,290 watts of power is consumed in doing this work. Finally, the motor
is capable of furnishing 10 hp or 7,460 watts at its shaft to do work.
The power equation may be used in three forms depending on the problems to be worked
P = EI; E = P/I; I = P/E
1. Determine the value of current in a 100 watt lamp on a 115 volt line.
I = P/E = 100/115 = 0.87 amp.
2. Determine the potential drop of a line which consumes 1,200 watts in carrying 60
E = P/I = 1,200/60 = 20 v.
3. Determine the power consumed by a 440 volt motor, if it draws 22 amperes.
P = E x I = 440 x 22 = 9,680 w.
4. What is the hp of the motor in question 3?
hp = P/746 = 9,680/746 = 13 hp
LARGE AND SMALL UNITS
You ordinarily would measure butter by the pound and coal by the ton. Think how clumsy
it would be to reverse this procedure - butter by the ton and coal by the pound. The
simple units of electrical measure - volts, amperes, ohms, and watts - prove to be clumsy
when very LARGE or extremely SMALL quantities are involved. A system of pre-fixes has
developed for use in measuring large and small quantities of electrical units. The table
below gives the common prefixes used in electricity. Each prefix can be used with any
of the electrical units. For example, instead of saying "a 10,000 watt generator," it
is handier to say "a 10 KILOWATT generator." Instead of writing "0.010 amperes" it is
easier to write "10 MILLIAMPERES." In testing insulation you will use MEGOHMS instead
of millions of ohms. In radio work, the MICRO- and MILLI- prefixes are constantly used.
MEGA ................ MILLION (1,000,000)
................. THOUSAND (1,000)
1 MILLI ..............
1 MICRO ............ ONE-MILLIONTH
Chapter 7 Quiz