AC/DC
ELECTRICAL
SYSTEMS
LEARNING
ACTIVITY
PACKET
CIRCUIT ANALYSIS
BB227-BC03UEN
LEARNING ACTIVITY PACKET 3
CIRCUIT ANALYSIS
INTRODUCTION
The previous LAP discussed how current, resistance, and voltage are affected by
circuits with series and parallel loads. It did not, however, attempt to analyze the precise
relationship among these three characteristics. This LAP will do just that through Ohm’s
Law and Kirchhoff’s voltage and current laws. These laws are fundamental concepts used
by every electrician, electronics technician, and electrical engineer.
One application of these laws is to determine how much power is needed for a circuit.
This LAP will explain this calculation.
ITEMS NEEDED
Amatrol Supplied
1
T7017 AC/DC Electrical Learning System
FIRST EDITION, LAP 3, REV. A
Amatrol, AMNET, CIMSOFT, MCL, MINI-CIM, IST, ITC, VEST and Technovate are trademarks or registered trademarks of Amatrol,
Inc. All other brand and product names are trademarks or registered trademarks of their respective companies.
Copyright © 2012 by AMATROL, INC.
All rights Reserved. No part of this publication may be reproduced, translated, or transmitted in any form or by any means, electronic,
optical, mechanical, or magnetic, including but not limited to photographing, photocopying, recording or any information storage and
retrieval system, without written permission of the copyright owner.
Amatrol,Inc., 2400 Centennial Blvd., Jeffersonville, IN 47130 USA, Ph 812-288-8285, FAX 812-283-1584 www.amatrol.com
BB227-BC03UEN CIRCUIT ANALYSIS
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TABLE OF CONTENTS
SEGMENT
1 POWER IN SERIES CIRCUITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
OBJECTIVE
SKILL
OBJECTIVE
SKILL
OBJECTIVE
1
1
2
2
3
SEGMENT
2 POWER IN PARALLEL CIRCUITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
OBJECTIVE
SKILL
OBJECTIVE
SKILL
SKILL
6
4
7
5
6
SEGMENT
3 CIRCUIT PROTECTION DEVICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
State the formula for calculating series resistance and give an application
Calculate series resistance given each load’s resistance
State Ohm’s Law, explain its importance and give an application
Use Ohm’s Law to calculate voltage, current, and resistance in a series circuit
State Kirchhoff’s voltage law for a series circuit and give an application
Activity 1 Verification of Kirchhoff’s Voltage Law
OBJECTIVE 4 Define power and give its units of measurement
OBJECTIVE 5 State a formula for calculating the total power used in an electrical circuit
SKILL 3 Calculate the total power used by a series circuit
OBJECTIVE 8
OBJECTIVE 9
SKILL 7
SKILL 8
OBJECTIVE 10
SKILL 9
SKILL 10
State Kirchhoff’s Current Law and give an application
Calculate the main line current in a parallel circuit
State a formula for calculating total parallel resistance
Calculate the total parallel resistance
Calculate the total power used in a parallel circuit
Describe the function of two types of circuit protection and give an application of each
Describe the operation of a fuse and give its schematic symbol
Operate a circuit using a fuse
Test and replace a fuse
Describe the operation of two types of circuit breakers and give their schematic symbols
Operate a circuit using a circuit breaker
Test and reset a circuit breaker
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SEGMENT 1
POWER IN SERIES CIRCUITS
OBJECTIVE 1
STATE THE FORMULA FOR CALCULATING SERIES RESISTANCE
AND GIVE AN APPLICATION
The total resistance in a circuit determines how much power the circuit will
draw. If the loads are connected in series, the total resistance can be calculated as
follows:
TOTAL RESISTANCE FOR SERIES
RT = R1 + R2 + R3 ....
where
RT
R1
R2
R3
=
=
=
=
total resistance in Ohms
resistance of R1 in Ohms
resistance of R2 in Ohms
resistance of R3 in Ohms
+24V
+
R1
R2
R3
R4
RT
Figure 1. Total Series Resistance Circuit
Knowing how to calculate series resistance is useful when designing a sound
system. Each speaker has a certain amount of resistance. When speakers are
connected in series, their total resistance is added. Care must be taken not to overload the amplifier by connecting an excessive load. Many times multiple speakers
are connected in series and parallel combinations to keep the total resistance within
an acceptable range.
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SKILL 1
CALCULATE SERIES RESISTANCE GIVEN EACH LOAD’S
RESISTANCE
Procedure Overview
In this procedure, you will calculate total resistance in a series circuit and
verify your calculations by measuring the total resistance.

1. Calculate the total resistance of the circuit in figure 2.
RT = _________________________________________________ (Ohms)
+
12V
R1 = 10
R2 = 25
R3 = 25
RT
Figure 2. Calculation of Total Resistance

The answer is found as follows:
RT = R1 + R2 + R3 ....
RT = 10 + 25 + 25
RT = 60

The total resistance for the circuit is 60 ohms.
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

2. Connect the series circuit shown in figure 3.
This will allow you to prove that the resistances add together in series.
NOTE
You will not need to connect the power supply to take the measurements
in this circuit.
R1 = 10
R2 = 25
R3 = 25
POINT A
POINT B
Figure 3. Series Circuit

3. Measure the resistance of each load.
Resistance R1 = ________________________________________ (Ohms)
Resistance R2 = ________________________________________ (Ohms)
Resistance R3 = ________________________________________ (Ohms)


R1 should be approximately 10 ohms, R2 should be approximately 25 ohms,
and R3 should be approximately 25 ohms.
4. Measure the total resistance by placing one lead at point A and the other lead
at point B.
Total resistance = _______________________________________ (Ohms)


The total resistance should be approximately 60 ohms. There might be a
slight variance.
5. Disconnect the circuit and store all components.
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OBJECTIVE 2
STATE OHM’S LAW, EXPLAIN ITS IMPORTANCE AND GIVE AN
APPLICATION
In the previous LAP, you saw that the current in series and parallel circuits is
affected when the resistance changes. An increase in resistance causes a decrease
in current and vice versa.
In electrical circuits where the loads are only resistance-type loads, the voltage,
current, and resistance are actually related to each other by a formula known as
Ohm’s Law.
Ohm’s Law says that one volt can push one amp of current through one ohm
of resistance. It is stated mathematically as follows:
OHM’S LAW
E=I×R
where
E = voltage (Volts)
I = current (Amps)
R = resistance (Ohms)
Ohm’s law allows you to calculate either voltage, current or resistance if you
know two of the three variables. For example, in figure 4, you can calculate the
current that will run through the circuit because the voltage (24 volts) and resistance (10 ohms) are known. This is calculated as follows:
E= I×R
24 = 1 × 10
I=
24
10
I = 2.4 Amps
24V
+
I
R=10
Figure 4. Ohm’s Law
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Ohm’s law is a fundamental electrical concept. If you work with electricity,
you will use it often.
Four applications of Ohm’s Law are:
• Troubleshooting Circuits - Ohm’s Law can be used to diagnose problems
in a circuit by comparing the actual voltage and current to the theoretical
values.
• Calculating Power Dissipation - Ohm’s Law can be used to determine how
much electrical power is needed to supply a circuit.
• Size Component - Ohm’s Law is used to size components and wires in
circuits.
• Create Multiple Voltage Levels - Ohm’s Law can be used to design a circuit
to supply a specific voltage that is lower than the source voltage. This can
be used for a device that needs a specific reference voltage.
SKILL 2
USE OHM’S LAW TO CALCULATE VOLTAGE, CURRENT,
AND RESISTANCE IN A SERIES CIRCUIT
Procedure Overview
In this procedure, you will calculate voltage, current, and resistance in a
series circuit by applying Ohm’s Law.

1. Calculate the power supply’s voltage for the circuit shown in figure 5 if the
current is 2 amps and resistor R1 has a resistance of 20 ohms.
+
E
I = 2A A
R1 = 20
Figure 5. Voltage Calculation
Voltage (E) = ____________________________________________ (Volts)

The solution to this problem is found by using Ohm’s law as follows:
E = I×R
E = 2A × 20 Ohms
E = 40 Volts
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

2. Calculate the voltage drop across resistor R1 in the circuit of figure 6.
The current and resistance are noted in the schematic diagram.
+
E1
I = 3A A
V
R1 = 10
R2 = 15
Figure 6. Voltage Calculation
E1 = ___________________________________________________ (Volts)


This is solved by using only the resistance of R1 in the Ohm’s law formula (E
= 3 × 10). The answer is 30 V.
3. Calculate the power supply’s voltage if the total circuit resistance is 25 ohms
and the current measured is 5.0 amps.
Voltage (E) = ____________________________________________ (Volts)

The answer is E = 125 volts.

In addition to using Ohm’s law to solve for voltage, you can also use it to
solve for current and resistance. In the applications of this unit, you will do
this more often because the T7017 power supply is a constant voltage power
supply. Therefore, you already know voltage.

To solve for resistance, rearrange Ohm’s law as follows:
E
I

To solve for current, rearrange Ohm’s law as follows:
E
R

= R
= I
In the remaining steps of this skill, you will use Ohm’s law to solve for current
and resistance.
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
4. Calculate the current in the circuit shown in figure 7. The power supply is a
constant voltage power supply.
Current (I) = ___________________________________________ (Amps)

The answer is I = 2.4 amps.
24 V
+
I
10
Figure 7. Current Calculation


Being able to calculate current in a circuit is important if you want to add a
circuit protection device. You must know the total current in order to select
the properly-rated protection device. If the current is much above the device’s
rating, the device will blow or trip when operated in the circuit, as you will
see later in this LAP.
5. Calculate the current in the circuit shown in figure 8 using the voltage and
resistance values.
Current = _____________________________________________ (Amps)

The answer is I = 2 Amps.
24V
+
3
9
Figure 8. Current Calculation

Since the total resistance is 12 ohms (3 + 9), the current is (24/12).
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
6. Calculate the resistance of the load in figure 9 if the voltage applied to the
circuit is 120V and the current is 3A.
R =___________________________________________________ (Ohms)

The answer is R = 40 ohms.
+
120V
I = 3A
R
Figure 9. Resistance Calculation


Knowing the resistance of a load is important in designing a circuit because
of the effect it has on the current and voltage. Sometimes loads do not specify
their resistance. However, Ohm’s Law gives us a means of determining an
unknown resistance value.
7. Calculate the resistance of the load shown in figure 10. The voltage and
current are shown.
Resistance = ___________________________________________ (Ohms)

The answer is R = 10 ohms.
+
I= 1.2A
12V
R
Figure 10. Resistance Calculation
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
8. Calculate the current in the circuit shown in figure 11.
Current = ______________________________________________ (Amps)
The answer is I = 0.80 Amps.
35V
+
I
12
5
20
7
Figure 11. Current Calculation

9. Calculate the unknown resistance value in the circuit shown in figure 12.
HINT
You will need to determine the voltage drop across both resistors.
Resistance = ___________________________________________ (Ohms)
The answer is R = 23 Ohms.
24V
+
I = .8A
R
7
Figure 12. Resistance Calculation
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OBJECTIVE 3
STATE KIRCHHOFF’S VOLTAGE LAW FOR A SERIES CIRCUIT AND
GIVE AN APPLICATION
Another important set of electrical relationships you often use is Kirchhoff’s
Laws. The first one you will learn is Kirchhoff’s Voltage Law.
Kirchhoff’s Voltage Law states that the total voltage in a series circuit is equal
to the sum of the individual voltage drops in the circuit. Stated in an equation
Kirchhoff’s Voltage Law would be as follows:
KIRCHHOFF’S VOLTAGE LAW
VT = VR1 + VR2 + VR3…
where
VT
VR1
VR2
VR3
=
=
=
=
total voltage in Volts
voltage drop across R1 in Volts
voltage drop across R2 in Volts
voltage drop across R3 in Volts
For example, in figure 13, the voltage drop across each resistor is shown.
Therefore, the total voltage of the circuit, according to Kirchhoff’s Voltage Law, is
24 V. This is equal to the power supply voltage.
+24V
+
R1
VR1=10V
R2
VR2=5V
VRT=24V
R3
VR1=9V
Figure 13. Example of Kirchhoff’s Voltage Law
This law is very important in the design and troubleshooting of multiple load
series circuits.
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Activity 1. Verification of Kirchhoff’s Voltage Law
Procedure Overview
In this procedure, you will measure the individual voltage drops across
each load in a series circuit and add them to verify Kirchhoff’s Voltage Law.

1. Connect the circuit in figure 14.
+
12V
R1 = 10
VR1
R2 = 25
R3 = 25
VR2
VR3
Figure 14. Example Circuit

2. Perform the following substeps to operate the circuit.
A. Place the AC/DC switch in the DC position.
B. Turn on the power supply.

3. Prepare the DMM to measure DC voltage.

4. Measure the voltage drop across each load.
Voltage Drop R1 = _______________________________________ (VDC)
NOTE
The larger the resistance value is, the larger the voltage drop is.
Voltage Drop R2 = _______________________________________ (VDC)
Voltage Drop R3 = _______________________________________ (VDC)


Voltage drop R1 should be approximately 2V, voltage drop R2 should be
approximately 5V, and voltage drop R3 should be approximately 5V.
5. Turn off the power supply, disconnect the circuit, and store all components.
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
6. Calculate the total voltage drop for the circuit.
Total Voltage Drop = _____________________________________ (VDC)


The total voltage drop should be approximately 12V.
7. Compare the total voltage drop to the source voltage.
Total Voltage Drop = _____________________________________ (VDC)
Source voltage = ________________________________________ (VDC)

OBJECTIVE 4
The total voltage drop should equal the source voltage, which is what
Kirchhoff’s Voltage Law says.
DEFINE POWER AND GIVE ITS UNITS OF MEASUREMENT
Power is the measure of the energy consumed by a circuit. It is measured in
watts, abbreviated W. One watt of energy is consumed when one volt pushes one
amp through a circuit.
OBJECTIVE 5 STATE A FORMULA FOR CALCULATING THE TOTAL POWER USED IN
AN ELECTRICAL CIRCUIT
The power used by any load in a circuit can be determined using the following
basic power formula:
POWER FORMULA
P=I×E
where
P = power (Watts)
I = current (Amps)
E = voltage (Volts)
This formula will work in either AC or DC circuits.
The Ohm’s law value for voltage, E = I × R, can be substituted and the formula
P = I × E = I × (I × R) and restated as:
ALTERNATE POWER FORMULA
P = I2 × R
where
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P = power (Watts)
I = current (Amps)
R = resistance (Ohms)
15
These two formulas can be used to calculate the power used by a single component or by the entire circuit. To calculate the power used by the entire circuit, E
equals the power supply’s voltage and I is the total current. R equals the total resistance, as shown in figure 15.
E=+24V
+
I=1A
8
8
8
RT = 24 OHMS
Figure 15. Circuit Power Output Calculation
The total power in a series circuit can also be calculated by adding together the
power used by each load. This can be stated as:
TOTAL POWER IN SERIES
PT = PR1 + PR2 + PR3....
where
BB227-BC03UEN CIRCUIT ANALYSIS
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PT
PR1
PR2
PR3
=
=
=
=
total power in Watts
power dissipation of R1 in Watts
power dissipation of R2 in Watts
power dissipation of R3 in Watts
16
SKILL 3
CALCULATE THE TOTAL POWER USED BY A SERIES CIRCUIT
Procedure Overview
In this procedure, you will calculate the total power used in a series circuit.
This is a common calculation designed to determine the sizes of components
needed in the circuit.

1. Calculate the total power used in the circuit shown in figure 16.
PT = ___________________________________________________ (Watts)

The solution is found as follows:

Since we know the total voltage and current, we can use the first power in
series formula.
PT = IT × ET
PT = .19 × 24
PT = 4.56 W
+
I = .19A
24V
R1 = 42
R2 = 42
R3 = 42
Figure 16. Total Power Calculation
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
2. Calculate the power used by the circuit shown in figure 17.
P = ____________________________________________________ (Watts)

Since the current and resistance are given, we can use the I2R formula as
follows:
P = I2 × R
P = (22) × 10
P = 40 watts
V
+
I = 2A
5
5
Figure 17. Total Power Calculation

3. Calculate the power used by the circuit shown in figure 18.
P = ____________________________________________________ (Watts)

The answer is 48 Watts.
24V
+
I = 2A
R
Figure 18. Total Power Calculation
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
4. Calculate the power used by the circuit shown in figure 19.
PT = ___________________________________________________ (Watts)

The answer is 108 Watts.
V
+
I=3A
2
10
Figure 19. Total Power Calculation

5. Calculate the power used by the circuit shown in figure 20 using the total
resistance.
PT = ___________________________________________________ (Watts)

The answer is 24 Watts.
+
I= 2A
R1 = 2
R2 = 4
Figure 20. Total Power Calculation
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

6. Perform the following substeps to calculate the total power used in the
circuit shown in figure 20 by calculating the individual power used by each
component.
Figure 20 shows a circuit with the current and each resistance given. The
source voltage is not known.
A. Calculate the power dissipation of R1.
PR1 = I2 × R1
PR1 = 22 × 2
PR1 = ________________________________________________ (Watts)
The power used by R1 is 8 watts.
B. Repeat substep A for R2.
PR2 = ________________________________________________ (Watts)
The power dissipation of R2 is 16 watts.
C. Calculate the total power dissipation by adding the individual power
dissipations.
PT =_________________________________________________ (Watts)
The answer is found as follows:
PT = PR1 + PR2
PT = 8W + 16W
The total power used is 24 watts. This should be the same as you calculated in step 5.

7. Calculate the total power used by the circuit shown in figure 21.
PT = ___________________________________________________ (Watts)

The answer is 180 Watts.
I = 1.5A
R1 = 47
R2 = 33
Figure 21. Total Power Calculation
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SEGMENT 1
SELF REVIEW
1. __________ Law states that one volt can push one amp through one
ohm of resistance.
2. ___________ Voltage Law states that the total voltage in a series circuit
is equal to the sum of the individual voltage drops in the circuit.
3. The mathematical statement of Ohm’s Law is __________.
4. One way to calculate total power used in a series circuit is to multiply
the total voltage and total __________.
5. The total ______________ in a circuit determines how much power
the circuit will draw.
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SEGMENT 2
POWER IN PARALLEL CIRCUITS
OBJECTIVE 6
STATE KIRCHHOFF’S CURRENT LAW AND GIVE
AN APPLICATION
Another of Kirchhoff’s electrical laws is Kirchhoff’s Current Law, which
applies to parallel circuits.
Kirchhoff’s Current Law states that the amount of current flowing from the
power supply is equal to the current flowing back to the power supply. In a parallel
circuit, the total current that flows from and back to the power supply is called the
main line current.
As shown in figure 22, the main line current splits at node 1 with part of it
flowing through each branch. These branch currents then recombine at node 2 to
form the main line current again.
MAIN LINE
CURRENT (IT)
NODE 1
+
BRANCH
CURRENT
MAIN LINE
CURRENT (IT)
BRANCH
CURRENT
NODE 2
Figure 22. Main Line and Branch Currents
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From Kirchhoff’s Current Law, we can deduce that the main line current will
be equal to the sum of the currents in the branches. This is stated mathematically
as:
KIRCHHOFF’S CURRENT LAW FORMULA
IT = IR1 + IR2 + IR3....
where IT = total current (Amps)
IR1, IR2, IR3 = current of each branch (Amps)
As an example, in figure 23, the main line current is 6 amps. The branch
currents are 2 and 4 amps, which adds up to a total of 6 amps.
This differs from series circuits where the current is the same at every point in
the circuit. Kirchhoff’s Current Law also applies to AC circuits.
MAIN LINE = 6A
+
V
R1
BRANCH A
= 2A
R2
BRANCH B
=4A
Figure 23. Kirchhoff’s Current Law
One of the common applications of Kirchhoff’s Current Law is in house wiring
systems. As appliances and devices are added to the circuit, the main line current is
increased because all of the items are in parallel.
A special circuit protection device called a circuit breaker is installed in the
main line to prevent the main line current from exceeding a certain level. Knowing
Kirchhoff’s Current Law will help to determine how many devices can be added to
a circuit without exceeding the limit.
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SKILL 4
CALCULATE THE MAIN LINE CURRENT IN
A PARALLEL CIRCUIT
Procedure Overview
In this procedure, you will calculate the total current in a parallel circuit
using Kirchhoff’s current law. You will then connect a circuit and measure the
current in each branch to verify your calculations.

1. Use Ohm’s Law to calculate the current in each branch of the circuit in figure
24.
Current I1 = ____________________________________________ (Amps)
Current I2 = ____________________________________________ (Amps)
Current I3 = ____________________________________________ (Amps)

They should be I1 = 1.2A, I2 = .48A, and I3 = .48A.
IT
I1
I3
I2
+
12V
R1 = 10
R2 = 25
R3 = 25
Figure 24. Main Line Current Calculation

2. Calculate the main line current using the branch currents you calculated in
step 1 and Kirchhoff’s Current Law.
IT = I1 + I2 +I3
Main line current = ______________________________________ (Amps)

It should be 2.16A.
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
3. Connect the circuit shown in figure 25.

4. Prepare the DMM to measure DC current.

Be sure you have the test leads connected to the correct terminals of the
DMM to measure current.

5. Place the AC/DC selector switch on the power supply in the DC position.

6. Perform the following substeps to measure the current in each branch of the
circuit, as shown in figure 25.
A. Connect the circuit shown in figure 25 with the meter connected to
measure current in branch 1.
Remember, the meter must be in series with the load.
SCHEMATIC
SOURCE SELECT
I1
IT
AC
I2
I3
DC
+
12V
24V
12V
12V
SELECTOR
SWITCH
MODULE
A
A
A
30XR
NON
CONTACT
VOLTAGE
MIN MAX
V
200
NOTE: THE METER IS SHOWN
CONNECTED IN
BRANCH 1 ONLY.
HOLD
600 OFF 600
200
20
V
20
2
200m
2
200m
200
2m
20M
2M
20m
200k
200m
20k
2k
200
10 A
1.5V 9V
200
BATT
BATT 1.5V
10 A
200m
2m 20m
A
mA
V
COM
10A
25 RESISTOR
OHM MODULE
A
600V
300V
BATT 9V
200mA
MAX
FUSED
10A MAX
FUSED
25 RESISTOR
OHM MODULE
CAT
CAT
MAX
600V
600V
10 RESISTOR
OHM MODULE
Figure 25. Parallel Circuit Current Measurement
B. Turn on the power and measure the current in branch 1.
Current I1 = _________________________________________ (Amps)
It should be approximately the same as the value you calculated in step 1.
C. Turn off the power supply.
D. Move the meter to branch 2, as shown in the schematic of figure 25.
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E. Turn on the power supply and measure current in branch 2.
Current I2 = _________________________________________ (Amps)
F. Turn off the power supply.
G. Move the meter to branch 3 as shown in the schematic of figure 25.
H. Turn on the power supply and measure the current in branch 3.
Current I3 = _________________________________________ (Amps)
It should be approximately the same as the values you calculated in step 1.
I. Turn off the power supply.

7. Place the DMM in the circuit as shown in figure 26 to measure the main line
current.

8. Turn on the power supply and record the current.
Main line current = ______________________________________ (Amps)

The main line current should approximately match the calculations you made
in step 2.
NOTE
There may be some variance in the measured values and the calculated
values depending on how close the actual resistance of each resistor is to the
theoretical value. The variance can be as much as + or - 10%.
A
IT
+
12V
I1
R1
=10
I2
I3
R2
=25
R3
=25
IT
Figure 26. Main Line Current Measurement


9. Turn off the power supply.
10. Disconnect the circuit and store the components.
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OBJECTIVE 7
STATE A FORMULA FOR CALCULATING
TOTAL PARALLEL RESISTANCE
The calculation of total resistance in a parallel circuit is different than in a
series circuit where the total resistance is equal to the sum of the resistances. The
formula used to calculate resistance in a parallel circuit is:
TOTAL PARALLEL RESISTANCE FORMULA
RT =
1
1
R1
+
1
R2
+
1
R3
where RT = total resistance in ohms
R1, R2, R3 = individual resistances in ohms
The result of this formula is that the total resistance of the parallel circuit actually decreases as you add more resistors in parallel. You will see this demonstrated
in the skill that follows. This is just the opposite of a series circuit.
RT
R1
R2
R3
Figure 27. Resistance in a Parallel Circuit
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SKILL 5
CALCULATE THE TOTAL PARALLEL RESISTANCE
Procedure Overview
In this procedure, you will calculate the total resistance of the circuit using
the parallel resistance formula. In the first step you will be given an example.

1. Calculate the total resistance of the circuit in figure 28.
RT = __________________________________________________ (Ohms)

The solution is found as follows:
RT =
1
1
+
R
RT =
R
2
3
1
1
+
150
RT =
1
+
R
1
RT =
1
1
1
+
300
100
1
0.007 + 0.0033 + 0.01
1
0.02
RT = 50Ω

The total resistance is 50 ohms.
IT = 0.24A
+
12V
R1=
150
R2=
300
R3=
100
Figure 28. Total Resistance Calculation
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NOTE
Each time another load is added to a parallel circuit, the effective resistance
is lowered. This is exactly the opposite effect of adding a load to a series circuit,
which would increase the effective resistance of that circuit.
This is the reason the main line current increases as more branches are
added. Since the total resistance is reduced, Ohm’s Law says that the current
must increase since the voltage is constant.

2. Calculate the total resistance of the parallel circuit shown in figure 29.
RT = _________________________________________________ (Ohms)

The total resistance should be 5.56 ohms. Notice that this is lower than any
one of the three individual resistances.
+
12V
R1 = 10
R2 = 25
R3 = 25
Figure 29. Total Resistance Calculation
BB227-BC03UEN CIRCUIT ANALYSIS
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
3. Now connect the circuit shown in figure 29.

Do not connect the circuit to the power supply.

Any time you make resistance measurements in a circuit, you should
disconnect the circuit from the power supply.

4. Measure the resistance of each branch of the circuit with the DMM.
Remember to disconnect one side of the load in that branch from the circuit
before measuring. Reconnect each load after you make your measurement.
R1 = _________________________________________________ (Ohms)
R2 = _________________________________________________ (Ohms)
R3 = _________________________________________________ (Ohms)


The resistances should be R1 = 10 ohms, R2 = 25 ohms, and R3 = 25 ohms.
5. Measure the total resistance of the circuit, as shown in figure 30.
Total resistance = _______________________________________ (Ohms)

It should be approximately 5.56 ohms, the same value you calculated earlier.
This shows that the formula for calculating parallel resistance works.
DISCONNECTED
SUPPLY
RT
R1=10
R2=25
R3=25
Figure 30. Total Resistance Measurement

6. Disconnect the circuit and store all components.
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SKILL 6
CALCULATE THE TOTAL POWER USED
IN A PARALLEL CIRCUIT
Procedure Overview
In this procedure, you will calculate the total power used in a circuit. This
calculation uses the same principles used to calculate the power in a series
circuit except that the calculation of total resistance is different.
In steps 1 and 2 you will be given some examples. Then you will do it
yourself.


1. Calculate the total power used in the circuit shown in figure 31.
The power in a parallel circuit can be calculated using any of the three
methods used for series circuits:
• Method A - Calculate total resistance of the parallel circuit and use the I2R
formula.
• Method B - Determine the total voltage and current and use the I × E
formula
• Method C - Calculate the power consumed by each component and add
them together, as follows:
PT = P1 + P2 + P3 + . . .
I = 3 AMPS
+
E = 24V
R1 =
R2 =
R3 =
Figure 31. Total Power Used by a Parallel Circuit
PT = ___________________________________________________ (Watts)

The total power used by this circuit is 72 watts.

Since the circuit in figure 33 shows the total voltage and current, method B (I
× E) can be used as follows:
PT = IT × ET
PT = 3 × 24
PT= 72 watts
BB227-BC03UEN CIRCUIT ANALYSIS
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
2. Perform the following substeps to calculate the total power used in the circuit
shown in figure 32.
I = 2A
+
R1 = 10
R2 = 25
Figure 32. Total Power Calculation
A. Calculate the total resistance, RT.
R =
T
1
1
R
1
+
1
R
2
RT = _________________________________________________ Ohms
The total resistance is approximately 7.14 ohms.
B. Calculate the total power.
PT = I2 × RT
PT =_________________________________________________ (Watts)
Your answer should be 28.6 watts.
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
3. Perform the following substeps to calculate the total power used in the circuit
shown in figure 33. Use method C to solve it.
+
20V
MAXIMUM
POWER
=80W
R1 =
50
R2 =
20
R3 =
10
Figure 33. Total Power Calculation
A. Calculate the current in each branch of the circuit.
IR1 = _______________________________________________ (Amps)
IR2 = _______________________________________________ (Amps)
IR3 = _______________________________________________ (Amps)
The current IR1 = 0.4A. The current IR2 = 1A. The current IR3 = 2A.
B. Now calculate the power dissipation of each load using the basic power
formula (P = I × E).
P1 = _______________________________________________ (Watts)
P2 = _______________________________________________ (Watts)
P3 = _______________________________________________ (Watts)
They should be PR1 = 8W, PR2 = 20W, and PR3 = 40W. Since this is a parallel
circuit, the voltage across each branch is equal to the source voltage.
C. Calculate the total power used by the circuit.
PT = P1 + P2 + P3
PT = _______________________________________________ (Watts)
The total power used should be 68W.
BB227-BC03UEN CIRCUIT ANALYSIS
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
4. Calculate the power used by the circuit shown in figure 34.
+
V = 24V
10W
25W
Figure 34. Total Power Calculation
PT = ___________________________________________________ (Watts)


Your answer should be 35 watts.
5. Calculate the power used by the circuit shown in figure 35.
10
I = 2A
30
+
15
Figure 35. Total Power Calculation
PT = ___________________________________________________ (Watts)


Your answer should be 20 Watts.
6. Solve the following design problem.

Determine how many 100W light bulbs can be connected to a common
commercial building’s circuit if the source voltage is 120 VAC and the
maximum current that can be provided is 20A.

HINT: What is the maximum output power that the source can provide with
the 20A limit?
BB227-BC03UEN CIRCUIT ANALYSIS
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SEGMENT 2
SELF REVIEW
1. The _____________ current is the total current in a parallel circuit.
2. Kirchhoff’s Current Law says that the amount of current flowing from
the source is always __________ to the current flowing back to the
source.
3. The total resistance of a parallel circuit __________ (increases/
decreases) as more resistors are added in parallel.
4. Each time another branch is added to a circuit, it will __________
(increase/decrease) the load on the power supply.
5. Kirchhoff’s Current Law says that the main line current will be equal
to the _________ of the currents in the branches.
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SEGMENT 3
CIRCUIT PROTECTION DEVICES
OBJECTIVE 8 DESCRIBE THE FUNCTION OF TWO TYPES OF CIRCUIT PROTECTION
AND GIVE AN APPLICATION OF EACH
High current can damage electrical components. This condition can occur
when too many loads are connected to the circuit or if a short circuit (short) occurs.
A short circuit occurs when there is a direct path with little or no resistance created
between the positive and negative terminals of the power supply, and therefore
potentially high, damaging current.
There are two types of devices commonly used to protect electrical components from high current:
• Fuse
• Circuit Breaker
Both of these devices interrupt the flow of current. The fuse is a low cost device
that must be replaced each time an overload or short circuit condition occurs. The
circuit breaker can be reset.
Figure 36. Fuse (Left) and Circuit Breaker (Right)
Fuses are used in applications where a problem rarely occurs. A car’s light
system is an example. Circuit breakers are used where overloads commonly occur.
A power supply and your house wiring are two examples.
BB227-BC03UEN CIRCUIT ANALYSIS
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OBJECTIVE 9
DESCRIBE THE OPERATION OF A FUSE AND GIVE ITS
SCHEMATIC SYMBOL
A fuse is a low cost protection device that is placed in series with an electrical
circuit to protect the power supply and the components from damage due to excess
current flow.
As shown in figure 37, a fuse consists of a conductive wire or metal foil strip
encased in a glass tube. When the current flow exceeds the rated value of the fuse,
the wire or foil strip melts and opens the circuit (the fuse is blown).
If a fuse is good, it has continuity just like an unbroken wire. However, if a
fuse is blown, there is no longer continuity. Figure 37 also shows the schematic
symbol for a fuse.
SCHEMATIC
SYMBOL
GLASS TUBE
ELEMENT
FUSE WIRE
METAL CAP
Figure 37. A Fuse and Its Schematic Symbol
Many electrical devices have fuses. They are one of the first things a technician
checks when troubleshooting a circuit. Fuses are easy to replace.
Fuses are rated for a maximum current value. If for some reason that maximum
value is exceeded, the fuse blows to protect the components of the circuit. Special
care needs to be taken to make sure that the properly rated fuse is installed to
provide the needed protection.
BB227-BC03UEN CIRCUIT ANALYSIS
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SKILL 7
OPERATE A CIRCUIT USING A FUSE
Procedure Overview
In this procedure, you will operate a circuit using a fuse for circuit
protection.

1. Connect the circuit as shown in figure 38.
SCHEMATIC
SOURCE SELECT
AC
DC
12 VAC
24V
12V
12V
FUSE
FUSE
MODULE
PUSH BUTTON
SWITCH
MODULE
PUSHBUTTON
SWITCH
LAMP
LAMP
MODULE
Figure 38. A Fuse in a Circuit

2. Perform the following substeps to operate the circuit.
A. Place the AC-DC selector switch in the AC position.
B. Turn on the power supply.
C. Press and hold the pushbutton switch.
Lamp status ________________________________________ (On/Off)
The lamp should come on.
BB227-BC03UEN CIRCUIT ANALYSIS
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D. Release the pushbutton switch.
Lamp status ________________________________________ (On/Off)
The lamp should go off.
Since the lamp did come on when the pushbutton switch was pressed, we
know that the fuse did not blow. If the fuse was blown, the lamp would not
have come on when the pushbutton switch was pressed.
E. Turn off the power supply.
Leave the circuit connected and continue to Skill 8.
SKILL 8
TEST AND REPLACE A FUSE
NOTE
This procedure is optional. Consult your instructor to determine whether
you should perform this procedure or not.
Procedure Overview
In this procedure, you will test a fuse to determine if it has blown and
replace it with the proper rated fuse if necessary.

1. Make sure the power supply is off.

2. Use a wire to short out the lamp, as shown in figure 39.
LAMP MODULE
12 VAC
FUSE
SHORTING
WITH A
WIRE
Figure 39. Shorting Out the Lamp
BB227-BC03UEN CIRCUIT ANALYSIS
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
3. Turn on the power supply.

4. Push the pushbutton switch.
Lamp status __________________________________________ (On/Off)

The light should not come on because the fuse is blown. The fuse is blown
because of the excessive current caused by the short circuit.

5. Release the pushbutton switch.

6. Turn off the power supply.

7. Check the fuse for continuity using the continuity tester of the DMM.
Fuse status ____________________________ (Continuity/No Continuity)


You should not hear a beep because the fuse does not have continuity. It is
blown.
8. Perform the following substeps to replace the blown fuse, as shown in figure
40.
A. Pry up on the end of the fuse using the tip of one of the test leads until the
end is completely free of the clip.
This is shown in step A of figure 40.
B. Pull the other end out of the clip as shown in step B of figure 40.
C. Place a new fuse into the clip as shown in step C of figure 40 and press
down until the fuse is secure. You should hear a snapping sound when the
fuse is “clipped”.
STEP A
STEP B
STEP C
TEST
LEAD
PRESS
DOWN
FUSE
PULL
UP
FUSE
CLIPS
Figure 40. Removing and Replacing a Fuse

9. Remove the wire shorting out the lamp.

10. Turn on the power supply.

11. Operate the pushbutton switch again.
Lamp status __________________________________________ (On/Off)

The light should come on and stay on. You have now successfully replaced
the fuse.
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
12. Release the pushbutton switch.

13. Perform the following substeps to turn OFF and secure the power supply.
A. Turn the power supply off.
B. Disconnect any wires or components connected to the output terminals of
the power supply and store them.
OBJECTIVE 10 DESCRIBE THE OPERATION OF TWO TYPES OF CIRCUIT BREAKERS
AND GIVE THEIR SCHEMATIC SYMBOLS
A circuit breaker performs the same protective service as a fuse. However, it
can be reset and used again. Just as a fuse blows, a circuit breaker opens or trips
when an excessive current is present.
Most circuit breakers are either thermally triggered (tripped due to heat caused
by excessive current) or magnetically triggered (tripped due to the strength of the
magnetic field created by excessive current). In some cases a circuit breaker is a
combination of both.
The thermally triggered type has a lag time (delay) before it trips because the
temperature must increase enough to trip the breaker.
The magnetically triggered type trips immediately when a surge of excessive
current is present. However, a slow increase in current may not cause the magnetically triggered breaker to trip. This is why it is better to have a circuit breaker that
uses both types.
Circuit breakers can have different types of reset switches, as shown in figure
41. Some have lever type resets, while some have pushbutton resets. You will be
using a circuit breaker with a lever reset.
Most newer homes and businesses use circuit breakers in their electrical
control panels. Figure 41 also shows a typical circuit breaker panel you would see
in a home or business.
ON
TRIPPED
OFF
RESET
PUSHBUTTON
RESET
LEVER TYPE
RESET
CIRCUIT BREAKER
PANEL BOX
Figure 41. Different Styles of Circuit Breaker Resets and a Typical Circuit Breaker Panel
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Figure 42 shows the schematic symbols for these circuit breakers.
MAGNETIC
THERMAL
THERMAL-MAGNETIC
Figure 42. Schematic Symbols for Circuit Breakers
SKILL 9
OPERATE A CIRCUIT USING A CIRCUIT BREAKER
Procedure Overview
In this procedure, you will connect and operate a circuit with a circuit
breaker as a protection device.

1. Connect the circuit shown in figure 43.
SCHEMATIC
+
SOURCE SELECT
AC
24V
DC
24V
12V
12V
CIRCUIT
BREAKER
CIRCUIT
BREAKER
MODULE
SWITCH
MODULE
25
25 RESISTOR
OHM MODULE
Figure 43. A Circuit with a Circuit Breaker
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
2. Perform the following substeps to operate the circuit.
A. Place the AC-DC selector switch in the DC position.
B. Turn on the power supply.
C. Energize (close) the knife switch and leave it closed.
Wait for about 30 seconds to see if the circuit breaker “trips” off.
Circuit breaker status _____________________ (Tripped/Not Tripped)
The circuit breaker should not trip because the 25 ohm resistor only draws
a current of 0.96A (I = E/R). This is below the 1 amp rating of the circuit
breaker.
D. Open the knife switch.

3. Turn off the power supply.

4. Replace the 25 ohm resistor with a 10 ohm resistor.

5. Repeat step 2 and observe the circuit breaker’s operation.
Circuit breaker status ________________________ (Tripped/Not Tripped)



The circuit breaker should now trip immediately. Now the current is 2.4
amps. Over twice the rating of the circuit breaker.
6. Turn off the power supply and open the knife switch.
Leave the circuit breaker tripped and continue to Skill 10.
BB227-BC03UEN CIRCUIT ANALYSIS
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SKILL 10
TEST AND RESET A CIRCUIT BREAKER
Procedure Overview
In this procedure, you will check a circuit breaker to see if it has tripped
by testing its continuity. You will also correct the problem that made the circuit
breaker trip and then reset the circuit breaker. This procedure is one that you
might perform at home if one of the circuit breakers in your circuit breaker
panel tripped.

1. Make sure the T7017 power supply is off.

2. Prepare the DMM to measure continuity using the continuity function.

3. Test the circuit breaker for continuity by measuring across it’s terminals.
Circuit breaker status ________________________ (Tripped/Not Tripped)

You should not hear a beep because there is no continuity.

The breaker has been tripped.

4. Replace the 10 ohm resistor with a 25 ohm resistor.

5. Reset the circuit breaker by pushing the lever up into the ON position.

6. Retest the circuit breaker for continuity.
Circuit breaker status ________________________ (Tripped/Not Tripped)

You should now find that there is continuity, which means that the circuit
breaker is not tripped.

7. Turn on the power supply.

8. Energize (close) the knife switch and leave it closed.

Wait to see if the circuit breaker “trips” off.
Circuit breaker status ________________________ (Tripped/Not Tripped)



The circuit breaker should not trip. Once again the current is below the rating
of the circuit breaker.
9. Open the knife switch.
10. Perform the following substeps to turn off and secure the power supply.
A. Turn off the power supply.
B. Unplug the power cord from the wall outlet.
C. Disconnect any wires that may be connected to the power supply output
terminals.

11. Turn off the DMM, remove the test leads and store them.
BB227-BC03UEN CIRCUIT ANALYSIS
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SEGMENT 3
SELF REVIEW
1. A(n) ______ consists of a conductive wire or metal foil strip encased
in a glass tube.
2. When the current flow exceeds the rated value of the fuse, the fuse will
_______.
3. If a fuse is blown, there is no longer _________________.
4. The difference between a fuse and a circuit breaker is that a circuit
breaker can be _______ and used again, while a fuse cannot.
5. A thermally-triggered circuit breaker will have a delay time before it
trips because the _________ must build up.
6. A magnetically-triggered circuit breaker will trip immediately when
a(n) _______ of excessive current is present.
7. Most newer homes and businesses use _______________ in their
electrical control panels.
8. A(n) ______________ occurs when there is a direct path with little or
no resistance created between the positive and negative terminals of a
power supply.
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