Download DETERMINING TOTAL RESISTANCE IN A PARALLEL

OBJECTIVES
After studying Chapter 6, the reader should be able to:
1. Prepare for ASE Electrical/Electronic Systems
(A6) certification test content area “A” (General
Electrical/Electronic Systems Diagnosis).
2. Identify a parallel circuit.
3. Explain parallel circuit laws.
4. Calculate voltage drops in a parallel circuit.
5. State Kirchhoff’s current law.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
PARALLEL CIRCUITS
• A parallel circuit is a complete circuit that has more
than one path for the current.
• The separate paths which split and meet at junction
points are called branches, legs, or shunts.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
KIRCHHOFF’S CURRENT LAW
• Kirchhoff’s current law
(his first law) states:
– The current flowing into any
junction of an electrical circuit
is equal to the current flowing
out of that junction.
FIGURE 6-1 The amount of
current flowing into junction point
A equals the total amount of
current flowing out of the
junction.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
PARALLEL CIRCUIT LAWS
• Law 1 The total resistance of a parallel circuit is
always less than that of the smallest-resistance leg.
• Law 2 The voltage is the same for each leg of a
parallel circuit.
• Law 3 The sum of the individual currents in each
leg will equal the total current.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
PARALLEL CIRCUIT LAWS
FIGURE 6-2 The current in a parallel circuit splits (divides)
according to the resistance in each branch.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
DETERMINING TOTAL RESISTANCE IN A
PARALLEL CIRCUIT
• There are five methods commonly used to determine total
resistance in a parallel circuit.
• Method 1
– The total current (in amperes) can be calculated first by treating each
leg of the parallel circuit as a simple circuit.
FIGURE 6-3 In a typical parallel circuit, each resistance has power
and ground and each leg operates independently of the other legs of the circuit.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
DETERMINING TOTAL RESISTANCE IN A
PARALLEL CIRCUIT
• Method 2
– If only two resistors are connected in parallel, the total resistance (RT)
can be found using the formula RT (R1 x R2) / (R1 + R2).
FIGURE 6-4 A schematic showing two resistors in
parallel connected to a 12 volt battery.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
DETERMINING TOTAL RESISTANCE IN A
PARALLEL CIRCUIT
• Method 3
– A formula that can be used to find the total resistance for any number
of resistances in parallel is 1 ÷ RT = 1 ÷ R1 + 1 ÷ R2 + 1 ÷ R3 . .
.
FIGURE 6-5 A parallel circuit with three resistors connected to a
12 volt battery.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
DETERMINING TOTAL RESISTANCE IN A
PARALLEL CIRCUIT
• Method 4
– Instead of determining the lowest common denominator
as in method 3, one can use the electronic calculator to
convert the fractions to decimal equivalents.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
DETERMINING TOTAL RESISTANCE IN A
PARALLEL CIRCUIT
FIGURE 6-6 Using an electronic
calculator to determine the total
resistance of a parallel circuit.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
FIGURE 6-7 Another example of how to use an
electronic calculator to determine the total
resistance of a parallel circuit. The answer is
13.45 ohms. Notice that the effective resistance
of this circuit is less than the resistance of the
lowest branch (20 ohms).
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
DETERMINING TOTAL RESISTANCE IN A
PARALLEL CIRCUIT
• Method 5
– This method can be easily used when two or more resistances
connected in parallel are of the same value.
FIGURE 6-8 A parallel circuit containing four 12 ohm resistors. When
a circuit has more than one resistor of equal value, the total resistance
can be determined by simply dividing the value of the resistance (12
ohms in this example) by the number of equal-value resistors (4 in this
example) to get 3 ohms.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
PARALLEL CIRCUIT EXAMPLES
Example 1
FIGURE 6-9 Example 1.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
PARALLEL CIRCUIT EXAMPLES
Example 2
FIGURE 6-10 Example 2.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
PARALLEL CIRCUIT EXAMPLES
Example 3
FIGURE 6-11 Example 3.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
PARALLEL CIRCUIT EXAMPLES
Example 4
FIGURE 6-12 Example 4.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
SUMMARY
1. A parallel circuit, such as is used for all automotive
lighting, has the same voltage available to each
resistance (bulb).
2. The total resistance of a parallel circuit is always
lower than the smallest resistance.
3. The separate paths which split and meet at
junction points are called branches, legs, or
shunts.
4. Kirchhoff’s current law states: “The current flowing
into any junction of an electrical circuit is equal to
the current flowing out of that junction.”
5. There are five basic methods that can be used to
calculate the total resistance in a parallel circuit.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
REVIEW QUESTIONS
1. Why is the total resistance of a parallel circuit less
than the smallest resistance?
2. Why are parallel circuits (instead of series circuits)
used in most automotive applications?
3. What does Kirchhoff’s current law state?
4. What are three of the five ways to calculate the
total resistance of a parallel circuit?
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
1.
Two bulbs are connected in parallel to a 12 volt battery.
One bulb has a resistance of 6 ohms and the other bulb
has a resistance of 2 ohms. Technician A says that only the
2 ohm bulb will light because all of the current will flow
through the path with the least resistance and no current
will flow through the 6 ohm bulb. Technician B says that
the 6 ohm bulb will be dimmer than the 2 ohm bulb. Which
technician is correct?
a)
b)
c)
d)
Technician A only
Technician B only
Both Technicians A and B
Neither Technician A nor B
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
1.
Two bulbs are connected in parallel to a 12 volt battery.
One bulb has a resistance of 6 ohms and the other bulb
has a resistance of 2 ohms. Technician A says that only the
2 ohm bulb will light because all of the current will flow
through the path with the least resistance and no current
will flow through the 6 ohm bulb. Technician B says that
the 6 ohm bulb will be dimmer than the 2 ohm bulb. Which
technician is correct?
a)
b)
c)
d)
Technician A only
Technician B only
Both Technicians A and B
Neither Technician A nor B
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
2. Calculate the total resistance and current in a
parallel circuit with three resistors of 4 , 8 , and 16
, using any one of the five methods (calculator
suggested). What are the values?
a)
b)
c)
d)
27 ohms (0.4 ampere)
14 ohms (0.8 ampere)
4 ohms (3.0 amperes)
2.3 ohms (5.3 amperes)
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
2. Calculate the total resistance and current in a
parallel circuit with three resistors of 4 , 8 , and 16
, using any one of the five methods (calculator
suggested). What are the values?
a)
b)
c)
d)
27 ohms (0.4 ampere)
14 ohms (0.8 ampere)
4 ohms (3.0 amperes)
2.3 ohms (5.3 amperes)
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
3. If an accessory such as an additional light is
spliced into an existing circuit in parallel, what
happens?
a)
b)
c)
d)
The current increases in the circuit.
The current decreases in the circuit.
The voltage drops in the circuit.
The resistance of the circuit increases.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
3. If an accessory such as an additional light is
spliced into an existing circuit in parallel, what
happens?
a)
b)
c)
d)
The current increases in the circuit.
The current decreases in the circuit.
The voltage drops in the circuit.
The resistance of the circuit increases.
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
4. A 6-cylinder engine uses six fuel injectors
connected electrically in two groups of three
injectors in parallel. What would be the resistance
if the three 12 ohm injectors were connected in
parallel?
a)
b)
c)
d)
36 ohms
12 ohms
4 ohms
3 ohms
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
4. A 6-cylinder engine uses six fuel injectors
connected electrically in two groups of three
injectors in parallel. What would be the resistance
if the three 12 ohm injectors were connected in
parallel?
a)
b)
c)
d)
36 ohms
12 ohms
4 ohms
3 ohms
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
5. A vehicle has four taillight bulbs all connected in
parallel. If one bulb burns out (opens), the current
flow in the circuit _____.
a) Increases and the other bulbs get brighter
b) Decreases because only three bulbs are operating
c) Remains the same because all the bulbs are wired in
parallel
d) Drops to zero and the other three bulbs go out
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
5. A vehicle has four taillight bulbs all connected in
parallel. If one bulb burns out (opens), the current
flow in the circuit _____.
a) Increases and the other bulbs get brighter
b) Decreases because only three bulbs are operating
c) Remains the same because all the bulbs are wired in
parallel
d) Drops to zero and the other three bulbs go out
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
6. Two identical bulbs are connected to a 12 volt
battery in parallel. The voltage drop across the
first bulb is 12 volts as measured with a voltmeter.
What is the voltage drop across the other bulb?
a)
b)
c)
d)
0 volt
1 volt
6 volts
12 volts
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
6. Two identical bulbs are connected to a 12 volt
battery in parallel. The voltage drop across the
first bulb is 12 volts as measured with a voltmeter.
What is the voltage drop across the other bulb?
a)
b)
c)
d)
0 volt
1 volt
6 volts
12 volts
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
7. Three resistors are connected to a 12 volt battery
in parallel. The current flow through each resistor
is 4 amperes. What is the value of the resistors?
a)
b)
c)
d)
1 ohm
2 ohms
3 ohms
4 ohms
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
7. Three resistors are connected to a 12 volt battery
in parallel. The current flow through each resistor
is 4 amperes. What is the value of the resistors?
a)
b)
c)
d)
1 ohm
2 ohms
3 ohms
4 ohms
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
8.
Two bulbs are connected to a 12 volt battery in parallel.
Another bulb is added in parallel. Technician A says that
the third bulb will be dimmer than the other two bulbs due
to reduced current flow through the filament of the bulb.
Technician B says that the amount of current flowing from
the battery will decrease due to the extra load. Which
technician is correct?
a)
b)
c)
d)
Technician A only
Technician B only
Both Technicians A and B
Neither Technician A nor B
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
8.
Two bulbs are connected to a 12 volt battery in parallel.
Another bulb is added in parallel. Technician A says that
the third bulb will be dimmer than the other two bulbs due
to reduced current flow through the filament of the bulb.
Technician B says that the amount of current flowing from
the battery will decrease due to the extra load. Which
technician is correct?
a)
b)
c)
d)
Technician A only
Technician B only
Both Technicians A and B
Neither Technician A nor B
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
9.
A vehicle has four parking lights all connected in parallel
and one of the bulbs burns out. Technician A says that this
could cause the parking light circuit fuse to blow (open).
Technician B says that it would decrease the current in the
circuit. Which technician is correct?
a)
b)
c)
d)
Technician A only
Technician B only
Both Technicians A and B
Neither Technician A nor B
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
9.
A vehicle has four parking lights all connected in parallel
and one of the bulbs burns out. Technician A says that this
could cause the parking light circuit fuse to blow (open).
Technician B says that it would decrease the current in the
circuit. Which technician is correct?
a)
b)
c)
d)
Technician A only
Technician B only
Both Technicians A and B
Neither Technician A nor B
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
10. Three resistors are connected in parallel to a 12
volt battery. The total current flow from the battery
is 12 amperes. The first resistor is 3 ohms and the
second resistor is 6 ohms. What is the value of the
third resistor?
a)
b)
c)
d)
1Ω
2Ω
3Ω
4Ω
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
CHAPTER QUIZ
10. Three resistors are connected in parallel to a 12
volt battery. The total current flow from the battery
is 12 amperes. The first resistor is 3 ohms and the
second resistor is 6 ohms. What is the value of the
third resistor?
a)
b)
c)
d)
1Ω
2Ω
3Ω
4Ω
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458
END
Diagnosis and Troubleshooting of Automotive Electrical,
Electronic, and Computer Systems, Fifth Edition
By James D. Halderman
© 2010 Pearson Higher Education, Inc.
Pearson Prentice Hall - Upper Saddle River, NJ 07458