NIDA SERIES 130E
Block 3
BASIC DC CIRCUITS
BASIC ELECTRICITY
UNIT I - DC CIRCUITS
LESSON 1
OHM'S LAW AND POWER
OBJECTIVES
OVERVIEW
On completion of this lesson, the student
will be able to:
This lesson is the first one in which
students study electrical circuit behavior.
1. State Ohm's Law and define the
relationship between current, voltage,
and resistance.
Ohm's Law is discussed, and the
relationship of current, voltage, and
resistance is analyzed.
2. Solve problems for unknown
quantities of current, voltage, and
resistance using Ohm's Law.
The three formulas that express the
relationship of current, voltage, and
resistance are presented.
3. Draw and use the circular expression
of Ohm's Law to help learn the Ohm's
Law formulas.
Students learn to use these three
formulas by solving problems for
unknown values of current, voltage, and
resistance.
4. Define power in an electrical circuit in
terms of current and voltage.
5. Demonstrate the ability to use Ohm's
Law with circuit measurements.
PREREQUISITES
None
EQUIPMENT REQUIRED
Nida Model 130E Test Console
Nida Series 130 Experiment Card
PC130-5
Nida Model 480/488 Multimeter, or
equivalent
Copyright © 2002 by Nida Corporation
Students learn to draw the circular
expression of Ohm's Law. They learn to
use this circle as a tool to help them learn
and remember the three Ohm's Law
formulas.
The relationship of power to current and
voltage is explained. The power formula
that expresses this relationship is
presented.
Students learn to use the power formula
to calculate the power in a circuit.
In the experiment, students measure
current, voltage, and resistance; and
solve problems to demonstrate their
understanding of Ohm's Law.
3-1-1
LESSON 1
OHM'S LAW AND POWER
UNIT I
Block 3
Basic DC Circuits
INTRODUCTION
The late 1700s and early 1800s saw a rapid growth in the development of new electrical
devices. One of these devices was the first battery made in 1796 by an Italian named
Volta.
A significant development came in 1827 by a German named George Simon Ohm, who
developed the relationship of current, voltage, and resistance in an electrical circuit. Ohm
announced this relationship in what became known as Ohm's Law.
Ohm's Law is perhaps the most important law in the study of electrical circuits, since the
relationship defined in the law is basic to all circuit operation. Memorize and learn how to
use Ohm's Law so that you build a strong foundation for your study of electronics.
VOLTAGE, CURRENT, AND RESISTANCE
Ohm's Law states the relationship of three electrical quantities: voltage, current, and
resistance. What are these three quantities? What do they do? How do we identify
them?
These questions are answered in Table 1, which lists the three quantities, their units of
measure, the symbols that identify them, and the function of each quantity in an electrical
circuit.
Table 1. Voltage, Current, and Resistance
QUANTITY
Name
UNIT OF MEASURE
Symbol
Name
Symbol
DEFINITION
Voltage
E
Volt
V
Voltage is the electrical pressure
or force which makes current
flow in a circuit.
Current
I
Ampere
A
Current is the flow of electrons
through a circuit.
Resistance
R
Ohm
Ω
Resistance is the opposition to
current flow offered by electrical
devices in a circuit.
Ohm's Law states:
OHM'S LAW
THE CURRENT (I) IN AN ELECTRICAL CIRCUIT IS
DIRECTLY PROPORTIONAL TO THE VOLTAGE (E) AND
INVERSELY PROPORTIONAL TO THE RESISTANCE (R).
3-1-2
Copyright © 2002 by Nida Corporation
Block 3
Basic DC Circuits
UNIT I
LESSON 1
OHM'S LAW AND POWER
The Ohm's Law relationship of current, voltage, and resistance is expressed in three
formulas:
I=
E
R
R=
Current equals
voltage divided
by resistance.
E
I
E= IR
Resistance equals
voltage divided
by current.
Voltage equals
current times
resistance.
In other words, what Ohm's Law means is that the current in an electrical circuit depends
on two things:
 The voltage applied to the circuit
 The resistance in the circuit
This relationship of current, voltage, and resistance in a circuit can be more easily
understood if you compare the circuits in Figure 1 and Figure 2.
The circuits in Figure 1 have a
fixed resistance. Note that when
the voltage increases, the current
also increases; when the voltage
decreases, the current also
decreases. The current,
therefore is directly proportional
to the voltage.
If you increase the voltage in a
circuit with a fixed resistance,
the current increases.
1A. Current Increases
If you decrease the voltage in a
circuit with a fixed resistance, the
current decreases.
1B. Current Decreases
Figure 1. Current is Directly Proportional To Voltage
Copyright © 2002 by Nida Corporation
3-1-3
LESSON 1
OHM'S LAW AND POWER
UNIT I
Block 3
Basic DC Circuits
Now look at Figure 2. The circuits in Figure 2 have a fixed voltage. Note that when the
resistance increases, the current decreases; when the resistance decreases, the current
increases. Thus, the current is inversely proportional to the resistance.
If you increase the resistance in a
circuit with a fixed voltage, the
current decreases.
2A. Current Decreases
If you decrease the resistance
in a circuit with a fixed
voltage, the current increases.
2B. Current Increases
Figure 2. Current is Inversely Proportional to Resistance
Example:
Ohm's Law and Voltage, Current, and Resistance.
Look at the electrical circuit in Figure 3. The
voltage source (E), a battery, is connected to
a resistive load (R) through a current meter
which will measure the current (I) of the
circuit.
How much current (I) flows in the circuit if
voltage (E) is 1 volt and resistance (R) is
1 ohm?
Figure 3. Electrical Circuit
Using Ohm's Law, you know the formula for I:
I=
E
R
Insert the values for voltage and resistance
into the formula, and solve for current:
I=
1V
=1 A
1Ω
The answer is that a voltage of 1 volt across a resistor of 1 ohm causes a current flow of
1 ampere.
3-1-4
Copyright © 2002 by Nida Corporation
Block 3
Basic DC Circuits
UNIT I
LESSON 1
OHM'S LAW AND POWER
What happens now, if you increase the voltage (E) to 12 volts but the resistance (R)
remains at 1 ohm? Does current increase or decrease?
Using Ohm's Law, you find that:
I=
E
R
=
12 V
1Ω
= 12 A
When voltage increases and resistance remains the same, current increases
proportionately to voltage.
Try one more. What happens if the voltage (E) remains at 12 volts, but the resistance (R)
increases to 24 ohms? Does current increase or decrease?
Again you use Ohm's Law:
I=
E
R
=
12 V
24 Ω
=
1V
2Ω
= 0.5 A
= 500 mA
As you can see, the current decreased.
Exercise 1:
Solve for an Unknown Quantity, Given Two Known Quantities.
Table 2 contains ten problems. Problem 1 has already been completed as an example.
Enter the your answers for the remaining problems in the appropriate blanks in the table.
Answers must include the basic unit of measure (V, A, or Ω).
Enter the formulas you use and your calculations in the appropriate columns. Use the
circuit diagram of Figure 3, if necessary, to help you visualize the circuit.
Table 2. Solve for the Unknown Quantities
NO.
1
VOLTAGE
CURRENT
RESISTANCE
12.0 V
3.0 A
4Ω
0.5 A
48 Ω
2
3
9.0 V
4
5
6.0 V
6
9.0 V
7
12.0 V
8
10.0 V
10
4.5 V
E
R
E = IR
CALCULATION
12
=3A
4
.5 x 48 = 24 V
E
I
1000 Ω
600 Ω
30.0 mA
1.2 kΩ
15.0 mA
9
I=
R=
3.0 A
0.045 A
FORMULA
1.0 kΩ
aA
Copyright © 2002 by Nida Corporation
18.0 kΩ
3-1-5
LESSON 1
OHM'S LAW AND POWER
UNIT I
Block 3
Basic DC Circuits
CIRCULAR EXPRESSION OF OHM'S LAW
The circular expression of Ohm's Law is a simple tool to aid you in learning and using
Ohm's Law. Figures 4A, 4B, 4C, and 4D illustrate the circle and how to use it.
The circle is
divided into 3
sections, as you
can see below: E
is in the top
section; I and R
are in the bottom
2 sections.
Put your finger
over I to solve
for current. You
see two letters
left: E over R, or
E divided by R.
I=
4A. The Circle
E
R
Put your finger
over R to solve
for resistance.
You see two
letters left: E
over I, or E
divided by I.
R=
4B. Current
E
I
Put your finger
over E to solve
for voltage. You
see two letters
left: I beside R,
or I times R.
E = IR
4C. Resistance
4D. Voltage
Figure 4. Circular Expression of Ohm's Law
POWER
Now that you understand the relationship of current, voltage, and resistance in electrical
circuits, you can learn about another important electrical quantity: power.
What is power? What does power do? How does power relate to current and voltage?
These questions are answered in Table 3.
Table 3. Power
QUANTITY
UNIT OF MEASURE
Name
Symbol
Name
Symbol
Power
P
Watt
W
DEFINITION
Power is the amount of work performed
by a circuit when the voltage forces
current to flow through the resistance.
In other words, power is the amount of work performed by an electrical circuit, and the
amount of work depends on how much voltage is required to force the current to flow
through the resistance. Thus, power is directly proportional to voltage and current.
3-1-6
Copyright © 2002 by Nida Corporation
Block 3
Basic DC Circuits
UNIT I
LESSON 1
OHM'S LAW AND POWER
Work performed by electrical circuits is in the form of heat which is generated when
voltage forces current to flow through resistance. This work can be either useful work or
nonuseful work.
Nonuseful work is heat produced by the resistors which adjust or control the amount of
current that flows in electrical circuits. The heat is not used and is simply an undesirable
byproduct of the resistors' function of controlling current. This use of power by resistors
to produce nonuseful heat is called power dissipation because the power is dissipated, or
given off, by the resistors.
With useful work, on the other hand, the purpose of the resistors in electrical circuits is to
generate heat rather than to control the current. In this case, the fact that resistors
control the current is a byproduct of their function of generating heat. Useful work is heat
produced by an electrical circuit to do such things as illuminate a light bulb to light up a
room or heat a toaster to toast bread.
You use electricity because you want it to do work for you, such as produce light. Take a
flashlight, for example. The electrical circuit of a flashlight consists of a battery to
generate the voltage which forces the current (controlled by a switch) to flow through a
resistor (a light bulb). This circuit is illustrated in Figure 5.
R is a light bulb.
E is a battery.
S is an ON/OFF switch.
Figure 5. Electrical Circuit of Flashlight
The work performed by the flashlight circuit results in the light produced by the light bulb.
The amount of light produced by the flashlight depends on how much voltage the battery
produces to force the current through the resistance of the light bulb. Thus, power (the
amount of work an electrical circuit performs) depends on how much voltage is needed to
force the current to flow through the resistance in the circuit.
As was stated before, power is directly proportional to voltage and current. This
relationship of power, voltage, and current can be stated in two ways:
1. One watt of power is used when 1 volt causes 1 ampere to flow through a circuit.
2. Power equals voltage times current: P = EI.
Copyright © 2002 by Nida Corporation
3-1-7
LESSON 1
OHM'S LAW AND POWER
Example:
UNIT I
Block 3
Basic DC Circuits
Solve for Power in an Electrical Circuit Using P = EI.
Assume that the voltage source for the flashlight in Figure 5 is two 1.5 V batteries, and
the resistance of the light bulb is 6 Ω.
You know the voltage of the 2 batteries:
E = 2 batteries x 1.5 V each = 3 V
You know the resistance of the light bulb:
R=6Ω
You do not know the current, so use
Ohm's Law to solve for current:
I=
Insert the values for E and I into the
formula for power:
P = EI = 3 V x 0.5 A
E 3V
=
= 0.5 A
R 6Ω
= 1.5 W
The flashlight uses 1.5 W of power.
This same problem can be solved in another, more direct way by using what is called the
substitution method.
Example:
Solve for Power in an Electrical Circuit using P = EI and
the Substitution Method.
You do not know the current, but you do know voltage and resistance.
You know the formula
I=
E
solves for current, using Ohm's Law.
R
Insert this formula for I into the
power formula for the unknown I:
P = EI and I =
Now insert the known values for E and R
into the power formula:
P = 3V×
3V
6Ω
E
R
so: P = E ×
=
9
W
6
E
R
= 1.5 W
The flashlight uses 1.5 W of power.
The power formula can be expressed in several ways, depending upon how you prefer to
write your formulas mathematically and upon what unknown quantity you have. The
example above shows the substitution of the Ohm's Law formula which solves for current
when current is unknown. When voltage is unknown, you substitute the Ohm's Law
formula which solves for voltage: E = IR.
Only some of the several ways for writing the power formula are given below. When you
solve for power, use whichever ones work best for you.
If current is unknown:
P = E (E ÷ R)
P = E×
P=
3-1-8
E2
R
E
R
If voltage is unknown:
P = I(IR)
P = I x IR
P = I2R
Copyright © 2002 by Nida Corporation
Block 3
Basic DC Circuits
UNIT I
LESSON 1
OHM'S LAW AND POWER
If you wish, you can memorize all these formulas. Memorizing them is not necessary,
however, if you just remember that P = EI and E = IR. You can derive any formula you
need from those two formulas.
Exercise 2:
Solve for Power, Given Two Known Quantities.
Here are a few problems to give you practice
solving for power. Show the formulas and
your calculations for all problems.
Use the circuit diagram in Figure 6, if
needed, to help you visualize the circuit.
Figure 6. Electrical Circuit
GIVEN
1. E = 12 V
R=6Ω
CALCULATIONS
P = EI
= E×
E
R
= 12 V ×
12 V
6Ω
= 24 W
2. I = 1.2 A
E = 1.5 V
3. I = 100 mA
E = 6 kV
4. E = 15 V
R = 100 Ω
5. R = 1 kΩ
I = 20 mA
6. I = 1.5 mA
E = 24.0 V
Copyright © 2002 by Nida Corporation
3-1-9
LESSON 1
OHM'S LAW AND POWER
UNIT I
Block 3
Basic DC Circuits
20. Calculate the percent of error for your current values in Table 4. Record your
answers in Table 4 (% ERROR).
Your calculations should show you that Ohm's Law and the relationship of current,
voltage, and resistance is valid, since the percent difference between your measured
values and your calculated values is within the expected limits of error.
21. Calculate the power that is dissipated in each of the three resistors on PC130-5 at all
the voltages applied, as shown in Table 4. Use your measured current values for
your calculations. Record your answers in Table 4 (POWER).
SUMMARY
In this lesson on Ohm's Law, you should have learned the following:
 Current in electrical circuits is directly proportional to the voltage in the circuit.
 Current in electrical circuits is inversely proportional to the resistance in the circuit.
 Ohm's Law is one of the most significant laws in electronics, since the relationship
defined in the law is basic to all circuit operation.
 The Ohm's Law relationship of current, voltage, and resistance in an electrical
circuit is expressed in the following formulas.
I=
E
R
E = IR
R=
E
I
 The circular expression of Ohm's Law is a tool you can use to help you remember
these three formulas.
 Power is the term which describes the amount of work an electrical circuit can do.
 Power is directly proportional to current and voltage.
 The power relationship of current and voltage is expressed in the following
formulas.
P = EI
3-1-14
P=
E2
R
P = I2R
Copyright © 2002 by Nida Corporation