Electrical Fundamentals-I
Module 3: Circuit Analysis
PREPARED BY
IAT Curriculum Unit
August 2012
© Institute of Applied Technology, 2012
ATE 310– Electrical Fundamentals-I
Module 3: Circuit Analysis
Module Objectives
Upon successful completion of this module, students should be able to:
1. Use Ohm’s Law to verify voltage, current, and resistance
measurement in a series circuit.
2. State Kirchhoff’s voltage law for a series circuit and give an
application.
3. State Kirchhoff’s Current Law and give an application.
4. Verify Kirchhoff’s laws through measurements.
5. Describe the function of two types of circuit protection and give an
application of each.
6. Describe the operation of a fuse and give its schematic symbol.
7. Describe the operation of two types of circuit breakers and give
their schematic symbols.
Module Contents:
Topic
Page No.
3.1
DC Series Circuit
3
3.2
DC Parallel Circuit
7
3.3
Circuit Protection Devices
10
3.4
Lab Activity 1
13
3.5
Lab Activity 2
15
3.6
Lab Activity 3
18
3.7
Review Exercise
20
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ATE 310– Electrical Fundamentals-I
3.1 DC Series Circuits
Calculating Series Resistance
As you have already learned in Physics, if the loads are connected in series,
the total resistance can be calculated as follows:
TOTAL RESISTANCE IN SERIES
!! ! !! ! !! ! !! !
Where, !! = total resistance in ohms
!! = resistance of R1 in ohms
!! = resistance of R2 in ohms
!! = resistance of R3 in ohms
Figure 3.1: Total Series Resistance Circuit
Example: Calculate the total resistance of the circuit in figure 3.2 below:
Total Resistance;
!! ! !! ! !! ! !!
!! ! !" ! !" ! !"
!! ! !" !
Figure 3.2: Calculation of Total
Resistance
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Ohm’s Law
In Module 2, 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 Physics, you have already seen that 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
! ! !!!
Where
V = 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.
Example: Calculate the current that will run through the circuit with
voltage (24 volts) and resistance (10 ohms).
! ! !!!
!" ! !!!"
Figure 3.3: Calculating Ohm’s Law
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Module 3: Circuit Analysis
!!!!!!!!!!!!!!!!!!!!!!!!!! !
!"
! !!!!!"#$
!"
ATE 310– Electrical Fundamentals-I
Kirchhoff’s Voltage Law for a Series Circuit
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
!! ! !!! ! !!! ! !!! !
Where;
!! = Total voltage in Volts
!!! = Voltage drop across !! in Volts
!!! = Voltage drop across !! in Volts
!!! = Voltage drop across !! in Volts
Example: Calculate the total voltage drop of the circuit.
!! ! !!! ! !!! ! !!! !
!! ! !" ! ! ! ! ! !"!
The total voltage drop is the same
as the supply voltage.
Figure 3.4: Kirchhoff’s Voltage Law
Power and Its Unit of Measurement
Power is the measure of the energy consumed by a circuit. It is measured
in watts, abbreviated W. The power used by any load in a circuit can be
determined using the following basic power formula:
POWER FORMULA
! ! !!!
Where;
! = Power in Watts, ! = Current in Amps,
! ! Voltage in Volts
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The Ohm’s law value for voltage, V = I " R, can be substituted and the
formula P = I " V = I " (I " R) restated as:
ALTERNATE POWER FORMULA
! ! ! ! !!
Where;
! = Power in Watts
! = Current in Amps
!= Resistance in Ohms
As covered under Physics, the total power in a series circuit can be
calculated by adding together the power used by each load.
TOTAL POWER IN SERIES
!! ! !!! ! !!! ! !!! !
Where;
!! = Total power in Watts
!!! = Power dissipation of !! in Watts
!!! = Power dissipation of !! in Watts
!!! = Power dissipation of !! in Watts
Conduct Lab Activity 1.
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3.2 DC Parallel Circuits
Calculating Parallel Resistance
As seen in Physics, the calculation of total resistance in a parallel circuit is
different than in a series circuit. The formula used to calculate resistance in
a parallel circuit is:
TOTAL PARALLEL RESISTANCE
!! !
!
!
!
!
!
!
!! !! !!
Where;
!! = Total resistance in Ohms
!! ! !! ! !! = Individual resistance 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.
Figure 3.8: Resistance in a Parallel Circuit
Example: Calculate the total resistance of the circuit in figure 3.9.
Figure 3.9: Total Resistance
Calculation
!! !
!
!
!
!
!! ! !! ! !!
!! !
!
!
!
!
!"# ! !"" ! !""
!! !
!
!!!!" ! !!!!"" ! !!!"
!! !
!
! !"#
!!!"
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Calculating the Total Power in Parallel Circuits
The power in a parallel circuit can be calculated using any of the three
formulas given below:
! ! ! ! !!
! ! ! ! !!!
!!!"#
Example: Calculate the total power of the circuit in figure 3.5.
Calculate the total resistance.
!! !
!
!
!
!! ! !!
!
!
!
!
!" ! !"
!! ! !!!"#
Calculate the total power
Figure 3.5: Total Power Calculation
!! ! ! ! !!! !
!! ! !!!!!" ! !"!!!
Kirchhoff’s Current Law
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 3.6, 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.
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Figure 3.6: Main Line and Branch Current
From Kirchhoff’s Current Law, 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
!! ! !!! ! !!! ! !!! !
Where;
!! = Total current in Amps
!!! ! !!! ! !!! = Current of each branch in Amps
Example: Calculate the main line current for the circuit given.
The main line current is:
!! ! !!! ! !!! ! !!! !
!! ! ! ! ! ! !!
Figure 3.7: Kirchhoff’s Current Law
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.
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.
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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.
Conduct Lab Activity 2.
3.3 Circuit Protection Devices
Two Types of Circuit Protection
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.
Since current flows through the path with least resistance, it will take this
path.
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 3.8: Fuse (Left) and Circuit Breaker (Right)
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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.
The Fuse Operation
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 3.9, 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 3.12 also shows the
schematic symbol for a fuse.
Figure 3.9: 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.
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Two Types of Circuit Breakers
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.
Circuit breakers can have different types of reset switches, as shown in
figure 3.10. 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 3.10 also shows a typical circuit breaker panel you
would see in a home or business.
Figure 3.10: Different Styles of Circuit Breaker Resets and a Typical Circuit
Breaker Panel
Conduct Lab Activity 3.
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3.4 Lab Activity 1
Objective:
To measure the individual voltage drops across each load in a series circuit
and add them to verify Kirchhoff’s Voltage Law.
Procedure:
1.
Connect the circuit in figure 3.11.
Figure 3.11: 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)
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.
6.
Calculate the total voltage drop for the circuit.
Total Voltage Drop = ________________________________ (VDC)
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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)
The total voltage drop should equal the source voltage, which is what
Kirchhoff’s Voltage Law says.
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3.5 Lab Activity 2
Objective:
To calculate and measure the current in a parallel circuit.
Procedure:
1.
Use Ohm’s Law to calculate the current in each branch of the circuit
in figure 3.12.
Current I1 = ______________________________________ (Amps)
Current I2 = ______________________________________ (Amps)
Current I3 = ______________________________________ (Amps)
They should be I1 = 1.2A, I2 = .48A, and I3 = .48A.
Figure 3.12: 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.
3.
Connect the circuit shown in figure 3.17.
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.
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Figure 3.13: Parallel Circuit Current Measurement
6.
Perform the following substeps to measure the current in each
branch of the circuit, as shown in figure 3.13.
A. Connect the circuit shown in figure 3.13 with the meter
connected to measure current in branch 1.
Remember, the meter must be in series with the load.
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 3.13.
E. Turn on the power supply and measure current in branch 2.
Current I2 = _______________________________ (Amps)
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F. Turn off the power supply.
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G. Move the meter to branch 3 as shown in the schematic of
figure 3.13.
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.
Figure 3.14: Main Line Current Measurement
7.
Place the DMM in the circuit as shown in figure 3.14 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.
9.
Turn off the power supply.
10.
Disconnect the circuit and store the components.
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3.6 Lab Activity 3
Objective:
To test and reset a circuit breaker.
Procedure:
1.
Connect the circuit as shown in Figure 3.15.
Figure 3.15: Circuit with a Circuit Breaker
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 = V/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.
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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.
7. Make sure the T7017 power supply is off.
8. Prepare the DMM to measure continuity using the continuity
function.
9. Test the circuit breaker for continuity by measuring across its
terminals.
Circuit breaker status _________________ (Tripped/Not Tripped)
You should not hear a beep because there is no continuity. The
breaker has been tripped.
10. Replace the 10 ohm resistor with a 25 ohm resistor.
11. Reset the circuit breaker by pushing the lever up into the ON
position.
12. 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.
13. Turn on the power supply.
14. 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.
15. Open the knife switch.
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16. 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.
17. Turn off the DMM, remove the test leads and store them.
3.7 Review Exercise
1.
___________ Voltage Law states that the total voltage in a series
circuit is equal to the sum of the individual voltage drops in the
circuit.
2.
Kirchhoff’s Current Law says that the amount of current flowing from
the source is always __________ to the current fl owing back to the
source.
3.
Kirchhoff’s Current Law says that the main line current will be equal
to the _________ of the currents in the branches.
4.
A(n) ______ consists of a conductive wire or metal foil strip encased
in a glass tube.
5.
When the current flow exceeds the rated value of the fuse, the fuse
will _______.
6.
If a fuse is blown, there is no longer _________________.
7.
The difference between a fuse and a circuit breaker is that a circuit
breaker can be _______ and used again, while a fuse cannot.
8.
Most new homes and businesses use _______________ in their
electrical control panels.
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