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Ch a pt er
4
Electrical Quantities
and Ohm’s Law
Learning Outcomes
Define electric current, voltage, resistance, power,
and energy, and list the unit of measurement of each.
Identify the essential parts of a circuit and state the
purpose of each.
In practical situations, you must be able to measure
electricity if you want to work with it. This chapter deals
with the standard units used for measuring of electric
voltage, current, resistance, power, and energy. It also
introduces Ohm’s law which defines the relationship
between voltage, current, and resistance.
Calculate different electric values using Ohm’s law.
State the difference between electron flow and
conventional current flow.
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Part 1 Current, Voltage, and
Resistance
Figure 4-2
4.1 Current
The coulomb is a measurement for a quantity of electrons, and the practical unit for an electric charge. One
coulomb of charge represents a total charge of 6.24 × 1018
(6,240,000,000,000,000,000) electrons. That appears to
be a lot, but only because the charge on one electron is
so small.
Charge in motion is referred to as current. Current is the
rate of flow of electrons through a conductor. The letter I
(which stands for intensity) is the symbol used to represent
current. Current is measured in amperes (A). The term ampere refers to the number of electrons passing a given point
in 1 second. If we could count the individual electrons, we
would discover that 1 ampere of current is equal to 1 coulomb of charge moving past a given point in 1 second, as
illustrated in Figure 4-1.
When the electrons begin to flow, the effect is felt instantly all along the conductor similar to the force that can
6.2
x 4
10 18
Electrons
per second
Figure 4-1
28
be transmitted through a row of billiard balls, as illustrated
in Figure 4-2. The electric current is actually the impulse
of electric energy that one electron transmits to another
as it changes orbit. The first electron repels the other out
of orbit, transmitting its energy to it. The second electron
repeats the action, and this process continues through the
conductor.
Although the individual electrons travel less than an
inch per second, the current effectively travels through the
conductor nearly at the speed of light (186,000 miles per
second). Because the atoms are close and the orbits overlap, the electron that is freed does not have to travel far to
encounter a new orbit. This action is almost instantaneous
so that even though the electrons are moving relatively
slowly, the electric current travels at almost the speed
of light.
An instrument called an ammeter is used to measure current flow in a circuit (Figure 4-3). The ammeter is inserted
into the path of the current flow, or in series, to measure current. This means the circuit must be opened and the meter
leads placed between the two open points.
Although the ammeter measures electron flow in coulombs per second, it is calibrated or marked in amps or
amperes. For most practical applications, the term amps is
used instead of coulombs per second when referring to the
1
and milli
amount of current flow. Prefixes micro _______
1,000,000
1
____
are
used
to
represent
very
small
amounts
of
current
1,000
and kilo (1,000) and mega (1,000,000) to represent very
large amounts as follows.
(
Measurement point
One ampere of current flow.
Transmission of electrons by impulse.
(
)
Units for Very
Small Amounts
)
Units for Very
Large Amounts
Current
Base Unit
Symbol
A
μA
mA
kA
MA
Pronounced As
Ampere
(Amp)
Microampere
Milliampere
Kiloampere
Megampere
Multiplier
1
0.000001
0.001
1,000
1,000,000
Section 1 Fundamentals of Electricity
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V
V
V
V
A
A
Ammeter
V
A
V
A
OFF
OFF
VV
A
VV
COM
Figure 4-5
Figure 4-3
Voltage (V, EMF, or E) is electric pressure, a potential
force or difference in electric charge between two points.
Voltage pushes current through a wire similar to water pressure pushing water through a pipe. The voltage level or value
is proportional to the difference in the electric potential energy between two points (Figure 4-4). Voltage is measured
in volts (V). A voltage of 1 volt is required to force 1 ampere
of current through 1 ohm of resistance. The letter E, which
stands for emf (electromotive force), or the letter V, which
stands for voltage, is commonly used to represent voltage in
an algebraic formula.
Voltage, or a difference in potential, exists between any
two charges that are not exactly equal to each other. Even
an uncharged body has a potential difference with respect
to a charged body; it is positive with respect to a negative
1 Volt
difference
between
charges
charge and negative with respect to a positive charge. Voltage also exists between two unequal positive charges or between two unequal negative charges. Therefore, voltage is
purely relative and is not used to express the actual amount
of charge, but rather to compare one charge to another and
indicate the electromotive force between the two charges
being compared.
A voltmeter is used to measure the voltage, or potential
energy difference of a load or source, as illustrated in Figure 4-5. Voltage exists between two points and does not flow
through a circuit as current does. It is possible to have voltage without current, but current cannot flow without voltage. A voltmeter is connected across, or in parallel, with the
two points.
Very small amounts of voltage are measured in milli1
1
and microvolts _______
, whereas high-voltvolts ____
1,000
1,000,000
age values are expressed in kilovolts (1,000) and megavolts
(1,000,000). The typical units of measurement are as
follows.
(
)
(
)
1 Ohm
resistance
1 Amp current
Voltage is proportional to the difference
between charges.
Voltage
Base
Unit
Symbol
V
Units for Very
Small Amounts
Units for Very
Large Amounts
μV
mV
kV
MV
Pronounced As Volt
Microvolt
Millivolt
Kilovolt
Megavolt
Multiplier
0.000001
0.001
1,000
1,000,000
Chapter 4
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Voltmeter connected to measure voltage.
Ammeter connected to measure current.
4.2 Voltage
Figure 4-4
COM
A
1
Electrical Quantities and Ohm’s Law
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4.3 Resistance
Resistance (R) is the opposition to the flow of electrons or
current. Basically, resistance is the measure of electric friction as electrons move through a conductor. Resistance is
measured in ohms. The Greek letter V (omega) is used to
represent ohms, and the typical units of measurement are as
follows.
example, a multimeter contains an ohmmeter that operates
by a battery located inside the instrument. The ohmmeter applies a known voltage into a circuit, measures the resulting
current, and then calculates the resistance. For this reason
ohmmeters should never be connected to live circuits!
PART 1 Review Questions
1. What is the practical unit of electric charge?
Resistance
Base
Unit
Symbol
Ω
Units for Very
Small Amounts
Units for Very
Large Amounts
μΩ
mΩ
Pronounced As Ohm
Microhm
Milliohm Kilohm
Megohm
Multiplier
0.000001
0.001
1,000,000
1
kΩ
1,000
MΩ
Resistance is due, in part, to each atom resisting the removal of an electron by its attraction to the positive nucleus.
Collisions of countless electrons and atoms as the electrons
move through the conductor create additional resistance.
The resistance created causes heat in the conductor when
current flows through it; that is why a wire becomes warm
when current flows through it. The higher the resistance of
a conductor, the greater its opposition to current flow. The
elements of an electric range become hot and the filament of
an incandescent lamp becomes extremely hot because they
have a much higher resistance than the conductors that carry
the current to them.
Every electric component has resistance, and this resistance
changes electric energy into another form of energy such as
heat, light, or motion. An ohmmeter is used to measure resistance, as illustrated in Figure 4-6. Unlike the voltmeter
and ammeter, which use energy in the current to make their
measurements, the ohmmeter uses its own power source. For
2. Define electric current.
3. What is the basic unit used to measure current?
4. Explain what a current flow of 1 ampere can be
equated to.
5. Account for the fact that electric current travels at the
speed of light, while the electron movement is relatively slow.
6. How must an ammeter be connected into a circuit to
measure current?
7. Define voltage.
8. What is the basic unit used to measure voltage?
9. Explain what a voltage of 1 volt can be equated to.
10. How must a voltmeter be connected into a circuit to
measure voltage?
11. Define electric resistance.
12. What is the basic unit used to measure resistance?
13. What is the cause and effect of resistance?
14. When using an ohmmeter to measure resistance,
what precaution must be observed?
15. Convert the following data:
a. 12,000 A to kA
b. 0.04 V to mV
c. 1.8 MΩ to Ω
d. 40 μA to A
V
V
A
V
Part 2
Power, Energy, and Ohm’s Law
A
OFF
VV
A
Figure 4-6
30
COM
Ohmmeter connected to measure resistance.
4.4 Power
Electric power (P) is the amount of electric energy converted to another form of energy in a given length of time.
Power represents the work performed by an electric circuit
and is measured in watts (W). Power in an electric circuit
is equal to
Power = voltage × current
Watts = volts × amperes
P = EI
Section 1 Fundamentals of Electricity
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Wattmeter
V
1440 W
120 V
12 A
Figure 4-7
I
100 W
Appliance power rating.
Figure 4-8
Wattmeter connected to measure power.
where
P = the power in watts
E = the voltage in volts
I = the current in amperes
The electric power rating of an appliance is listed on its
nameplate as illustrated in (Figure 4-7). This rating is not
always specified simply in terms of watts. Power rating may
be given in voltage and current, in which case, the power can
be calculated using the equation P = EI. When the rating is
given in watts and volts, the rated current can be calculated
using the equation
P
I = __
E
EXAMPLE 4-1
Problem: An iron draws 10 A from an 120-V household supply.
How much power is used?
motion, they have kinetic energy, or the energy of motion.
The unit of energy, called the joule (J), is used in scientific
work to measure electric energy. By definition, a joule is the
amount of energy carried by 1 coulomb of charge propelled
by an electromotive force of 1 volt.
The watt-hour (Wh) is the more practical unit of measurement of electric energy. Power and time are factors
that must be considered in determining the amount of energy used. This is usually done by multiplying watts by
hours. The result is watt-hours. If power is measured in
kilowatts and multiplied by hours, the result is kilowatthours, abbreviated kWh. Energy measurements are used
in calculating the cost of electric energy. A kilowatthour meter connected to a residential electrical system
is used to monitor your daily power usage as illustrated
in Figure 4-9.
Solution:
P = EI
= 120 V × 10 A
= 1,200 W, or 1.2 kW
Power can be measured using a wattmeter. The wattmeter is basically a voltmeter and ammeter combined into one
instrument (Figure 4-8). The ammeter terminals are connected in series, and the voltmeter terminals are connected
in parallel with the circuit in which the power is being measured. The wattage rating of a lamp indicates the rate at
which the device can convert electric energy into light. The
faster a lamp converts electric energy to light, the brighter
the lamp will be.
4.5 Energy
Electric energy refers to the energy of moving electrons.
In an operating electric circuit, the voltage pushes and
pulls electrons into motion. When electrons are forced into
Figure 4-9
Chapter 4
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Kilowatt-hour meter.
Electrical Quantities and Ohm’s Law
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Control device
(switch)
EXAMPLE 4-2
Problem: Assuming that the cost of electricity is 5 cents
($0.05) per kWh, how much will it cost to operate a 100-W lamp
continuously for 200 hours?
Power ⫺
source
(battery) ⫹
Solution:
100 W × 200 h
kWh = _____________
1,000
= 20 kWh
Conductor
(wire)
Load
device
(lamp)
Protective device
(fuse)
Cost = kWh × rate
= 20 × $0.05
Figure 4-11
Electric circuit schematic diagram.
= $1.00
4.6 Electric Circuit
The essential parts of an electric circuit consist of a power
source, protection device, conductors, control device, and
load. A closed circuit is a closed loop or path from one side
of a voltage source to the other, as illustrated in Figure 4-10.
A complete or closed circuit is needed for current to flow. If
the circuit is broken at any point, there is no longer a closed
loop and no current can flow. This is often referred to as an
open circuit.
Figure 4-11 shows the schematic diagram for an electric
circuit. A pictorial circuit diagram uses simple images of
components, while a schematic diagram shows the components of the circuit as simplified standard symbols; both
types show the connections between the devices. The function of the parts can be summarized as follows:
• Battery power source supplies the electric pressure or
voltage required to push current through the circuit.
• Conductors provide a low-resistance path from the
source to the load.
• Switch control device opens and closes the circuit to
switch the current flow OFF and ON.
• Lamp load converts the electric energy from the
power source into light and heat energy.
• Fuse protection device melts to automatically open the
circuit in the event of a higher than rated current flow.
Too much current can cause damage to conductors and
load devices.
Load device
Control
device
Electron
current flow
4.7 Ohm’s Law
Power
source
Figure 4-10
Ohm’s law defines the relationship between circuit current,
voltage, and resistance and is stated as follows: The current flowing in a circuit is directly proportional to the applied voltage and inversely proportional to the resistance.
Protection
device
Closed electric circuit.
Rated voltage
12 Volts
Lower voltage
6 Volts
2A
4A
3V
Figure 4-12
32
Higher voltage
18 Volts
3V
6A
3V
Effect of voltage on current flow.
Section 1 Fundamentals of Electricity
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12 Volts
12 Volts
12 Volts
4A
3V
Initial resistance
Figure 4-13
12 A
1A
1V
Lower resistance
12 V
Higher resistance
Effect of resistance on current flow.
Therefore, the higher the voltage applied to a circuit, the
higher the current through the circuit. On the other hand,
a decrease in the applied voltage will result in a decrease
in circuit current. This assumes that the circuit resistance
remains constant, as illustrated in Figure 4-12.
If the voltage is held constant, the current will change as
the resistance changes, but in the opposite direction. Assuming that voltage is constant, lowering the resistance causes
an increase in current. On the other hand, an increase in
resistance results in a decrease in current flow, as illustrated
in Figure 4-13.
Ohm’s law can be stated as mathematical equations, all
derived from the same principle as follows:
E (current = voltage divided by resistance)
I = __
R
E = I × R (voltage = current multiplied by resistance)
E (resistance = voltage divided by current)
R = __
I
EXAMPLE 4-4
Problem: If a 25-Ω resistor has a current flow of 2 A through
it, how much is the voltage across it?
Solution:
E = IR
= 2 A × 25 Ω
= 50 V
EXAMPLE 4-5
Problem: What is the resistance of a toaster element that is
rated for 120 V and 8 A?
Solution:
E
R = __
I
120
V
= ______
8A
EX A M P L E 4 -3
A portable heater with a resistance of 10 Ω is
plugged into a 120-volt electrical outlet. How much current will
flow to the heater?
Problem:
Solution:
= 15 Ω
4.8 Direction of Current Flow
E
I = __
R
120 V
= ______
10 Ω
= 12 A
The direction of current flow in a circuit can be designated
either as electron flow or conventional current flow, as illustrated in Figure 4-14. Electron flow is based on the electron
theory of matter and follows the motion of electrons in the
circuit from negative to positive. Conventional current
Electron flow
(negative to positive)
Figure 4-14
Conventional flow
(positive to negative)
Electron versus conventional current flow.
Chapter 4
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Electrical Quantities and Ohm’s Law
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flow is based on an older theory of electricity and assumes
a current flow in the opposite direction from positive to
negative.
Both conventional current flow and electron flow are acceptable and are used for different applications. For purposes
of circuit analysis it makes no difference which direction of
current flow you use as long as the same direction is used
consistently throughout the circuit. It is important to understand and be able to think in terms of both conventional current flow and in terms of electron flow.
PART 2 Review Questions
1. Define electric power.
2. What is the basic unit used to measure electric power?
3. A toaster draws 8 amperes when connected to a
120-volt source. What is the wattage rating of the
toaster?
7. Is it more expensive to operate a 1,000-W hair dryer
for 5 minutes or a 40-W lamp for 1 hour? Why?
8. Compare a closed and an open electric circuit.
9. State the function of each of the following components of a circuit:
a. Power source
b. Conductors
c. Control device
d. Protection device
e. Load
10. What does Ohm’s law tell us about current flow in a
circuit?
11. Ohm’s law is applied to a circuit using what three
mathematical equations?
12. A load has a resistance of 20 Ω. What is its current
when connected to 240 V?
13. How much resistance does a load have if it draws a
current of 6 A from a 12-V battery?
4. Explain why a 140-W soldering iron produces more
heat than a 20-W soldering iron.
14. A 12-Ω load is conducting a current of 2.5 amps.
How much is its voltage?
5. Define electric energy.
15. Compare the direction of electron flow and conventional current flow.
6. What is the basic unit used to measure electric energy?
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Section 1 Fundamentals of Electricity
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