chap33 pps Automotive technology at University of Cambridge

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Automotive Technology: Principles, Diagnosis, and Service, 3rd Edition
By James D. Halderman

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OBJECTIVES:
After studying Chapter 33, the reader should
be able to:

• Prepare for ASE Electrical/Electronic Systems
•
•
•
•

(A6) certification test content area “A” (General
Electrical/Electronic System Diagnosis).
Identify a series circuit.
State Kirchhoff’s voltage law.
Calculate voltage drops in a series circuit.
Explain series and parallel circuit laws.
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OBJECTIVES:

After studying Chapter 33, the reader should
be able to:

•
•

State Kirchhoff’s current law.
Identify where faults in a series-parallel
circuit can be detected or determined.

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KEY TERMS:
branches • combination circuit • compound circuit
Kirchhoff’s current law • Kirchhoff’s voltage law
leg • parallel circuit
series circuit • series-parallel circuits • shunt
total circuit resistance • voltage drop

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OHM’S LAW AND SERIES CIRCUITS

A series circuit is a complete circuit that has more than one 
electrical load where all of the current has only one path to flow 
through all of the loads.
Electrical components such as fuses and switches are generally not 
considered to be included in the determination of a series circuit. 
The circuit must be continuous or have continuity in order for 
current to flow through the circuit.

NOTE: An electrical load needs power and a ground to operate. A break 
(open) in a series circuit will cause the current in the circuit to stop.

Ohm’s law can be used to calculate the value of one unknown 
(voltage, resistance, or amperes) if the other values are known.
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Because all current flows through all resistances, total resistance is 
the sum (addition) of all resistances. 
Total resistance of the circuit 
shown here is 6 ohms
(1Ω = 2Ω + 3Ω).
The formula for total resistance 
(RT) for a series circuit is:

Using Ohm’s law to find
current flow: 
Continued

Figure 33–1 A series circuit with three bulbs. All
current flows through all resistances (bulbs). The
total resistance of the circuit is the sum of the
total resistance of the bulbs, and the bulbs will
light dimly because of the increased resistance
and the reduction of current flow (amperes)
through the circuit.

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With a total resistance of 6 ohms using a 12­volt battery in the
series circuit shown, 2 amperes of current will flow through the 
entire circuit. If resistance is reduced, more current will flow.
Here, one resistance has been 
eliminated and now the total resistance 
is 3 ohms (1Ω + 2Ω).
Using Ohm’s law to calculate current 
flow yields 4 amperes.

Figure 33–2
A series circuit with two bulbs.

Notice current flow was doubled  (4 amps 
instead of 2 amps) when the resistance 
was cut in half (from 6 ohms to 3 ohms).

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Farsighted Quality of Electricity
Electricity almost seems to act as if it “knows” what resistances are ahead
on the long trip through a circuit. If the trip through the circuit has many
high-resistance components, very few electrons (amperes) will choose to
attempt to make the trip.
If a circuit has little or no resistance (for example, a short circuit), then as

many electrons (amperes) as possible attempt to flow through the
complete circuit. If flow exceeds the capacity of the fuse or the circuit
breaker, then the circuit is opened and all current flow stops.

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KIRCHOFF’S VOLTAGE LAW
Voltage applied through a series circuit drops with each resistor. 
The greater the resistance, the greater the drop in voltage.
German physicist, Gustav Robert Kirchhoff (1824–1887), 
developed laws about electrical circuits. His second law, 

Kirchhoff’s voltage law, concerns voltage drops.
It states:

The voltage around any closed circuit is equal to the sum 
(total) of the voltage drops across the resistances.
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Applying Kirchhoff’s Voltage Law
Kirchhoff states in his
second law that voltage

drops in proportion to
resistance and the total
of voltage drops will
equal the applied
voltage. 

Figure 33–3 As current flows through a circuit, the voltage drops in proportion to the amount
of resistance in the circuit. Most, if not all, of the resistance should occur across the load such
as the bulb in this circuit. All of the other components and wiring should produce little, if any,
voltage drop. If a wire or connection did cause a voltage drop, less voltage would be available
to light the bulb and the bulb would be dimmer than normal.circuit with two bulbs.
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Total resistance of the circuit can be determined by adding the 
individual resistances (2Ω + 4Ω + 6Ω = 12Ω).
The current through the circuit is determined by using Ohm’s law,
I = E/R = 12V/12Ω = 1A.         
In the circuit shown, the 
following values are known:
Resistance = 12Ω
Voltage = 12V
Current = 1A

Continued
Automotive Technology: Principles, Diagnosis, and Service, 3rd Edition
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Figure 33–4 In a series circuit the voltage is
dropped or lowered by each resistance in the
circuit. The higher the resistance, the greater the
drop in voltage.

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Everything is known except the voltage drop caused by resistance. 
This can be determined by using Ohm’s law and calculating for 
voltage (E) using the value of each resistance individually:

According to Kirchhoff, the sum (addition) of the voltage drops 
should equal the applied voltage (battery voltage):
Total of voltage drops = 2V + 4V + 6V = 12V = Battery voltage
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NOTE: Notice that the voltage drop is proportional to the resistance.

Higher resistance means greater voltage drop. A 6­ohm resistance dropped 
the voltage three times as much as the drop created by 2­ohm resistance.

Another example of Kirchhoff’s 
second (voltage) law.
Figure 33–5
A voltmeter reads the differences of voltage
between the test leads. The voltage read
across a resistance is the voltage drop
that occurs when current flows through
a resistance.
A voltage drop is also called an “IR” drop
because it is calculated by multiplying the
current (I) through the resistance (electrical
load) by the value of the resistance ( R).

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Use of Voltage Drops  Due to built­in resistance, voltage drops are used in 
automotive electrical systems to drop the voltage in the following 
examples:

1. The Dash lights  Most vehicles are equipped with a method 
of dimming the brightness of the dash lights by turning a 
variable resistor. This type of resistor can be changed and 
therefore varies the voltage to the dash light bulbs. A high 
voltage to the bulbs causes them to be bright, and a low 
voltage results in a dim light.
2. The Blower motor (heater or air­conditioning fan). Speeds 
are usually controlled by a fan switch sending current 
through high­, medium­, or low­resistance wire resistors. 

Highest resistance will drop voltage the most, causing the 
motor to run at the lowest speed. Highest speed of the motor 
will occur when no resistance is in the circuit.
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Why Check Voltage Drop Instead of Resistance?
Imagine a wire with all strands cut except for one. An ohmmeter can be
used to check resistance of this wire and the resistance would be low,
indicating the wire was okay. But one strand cannot properly carry the
current (amps) in the circuit. A voltage drop test is better for two reasons:

•

An ohmmeter can only test a wire or component that has been
disconnected from the circuit and is not carrying current. The resistance
can, and does, change when current flows.

•

A voltage drop test is a dynamic test because as the current flows
through a component, the conductor increases in temperature, which in
turn increases resistance. This means that a voltage drop test is testing
the circuit during normal operation and is therefore the most accurate
way of determining circuit conditions.
A voltage drop test is also easier to perform because the resistance
does not have to be known, only that unwanted loss of voltage in a
circuit should be less than 3% or, about 0.14 volts for any 12-volt circuit.
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SERIES CIRCUIT LAWS
Law 1  Total resistance in a series circuit is the sum total of the 
individual resistances. The resistance values of each electrical load are 
simply added together.
Law 2  The current is constant throughout the entire circuit. If 2 amperes 
of current leave the battery, 2 amperes of current return to the battery.
Figure 33–6 In this series circuit with a 2-ohm resistor and a 4-ohm resistor, current (2
amperes) is the same throughout even though the voltage drops across each resistor.

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Law 3  Although current (in amps) is constant, voltage drops across 
each resistance in the circuit. The voltage drop across each load is 
proportional to the value of the resistance compared to the total 
resistance.
For example, if the resistance is one­half of the total resistance, the 
voltage drop across that resistance will be one­half of the applied 
voltage.
The sum total of all individual voltage drops equals the applied 
source voltage.

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SERIES CIRCUIT EXAMPLES
Each of the four examples includes solving for the following: 
Total resistance in the circuit
Current flow (amperes) through the circuit
Voltage drop across each resistance

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The unknown in this problem is the value of R2. The total 
resistance, however, can be calculated using Ohm’s law.
RTotal = E/I = 12 volts/3A = 4Ω

Because R1 is 3 ohms
and the total resistance
is 4 ohms, the value
of R2 is 1 ohm.

Figure 33–7 Example 1.
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The unknown in this problem is the value of R3. The total 
resistance, however, can be calculated using Ohm’s law.
RTotal = E/I = 12 volts/2 A = 6Ω
Total resistance of R1
(3 ohms) and R2 (1 ohm) 
equals 4 ohms so the
value of R3 is the 
difference between the 
total resistance (6 ohms) 
and the value of known 
resistance (4 ohms).
6 – 4 = 2 ohms = R3
Figure 33–8 Example 2.
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The unknown in this problem is voltage of the battery. To solve for 
voltage, use Ohm’s law (E = I × R). The “R” in this problem refers 
to the total resistance (RT). The total resistance of a series circuit is 
determined by adding the values of the individual resistors.
RT = 1Ω + 1Ω + 1Ω
RT = 3Ω 
Placing total resistance 
(3Ω) into the equation 
results in battery
voltage of 12 volts.
E = 4A × 3Ω
E = 12 volts 

Figure 33–9 Example 3.
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The unknown in this example is the current (amperes) in the circuit. 
To solve for current, use Ohm’s law.
I = E/R = 12 volts/6 ohms = 2A
Notice that the total 
resistance in the circuit 
(6 ohms) was used in 

this example, which is 
the total of the three 
individual resistors:
(2Ω + 2Ω + 2Ω = 6Ω)
The current through the 
circuit is two amperes.
Figure 33–10 Example 4.
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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. 
The current flow through each branch or leg varies depending on 
the resistance in that branch.
A break or open in one leg or section of a parallel circuit does not 
stop current flow through the remaining legs of the circuit.

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KIRCHOFFS CURRENT LAW

Kirchhoff’s current law (first law) states:
The current flowing into any junction of 
an electrical circuit is equal to the
current flowing out of that junction.
Illustrated using Ohm’s law, seen here: 
The 6­ohm leg requires 2 amps and the 
3­ohm resistance leg requires 4 amps.
The wire from the battery to junction A 
must be capable of handling 6 amps. 
The sum of current flowing out is equal
to current flowing into the junction, 
proving Kirchhoff’s current law.
Automotive Technology: Principles, Diagnosis, and Service, 3rd Edition
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Figure 33–11 The amount of current
flowing into junction point A equals
the total amount of current flowing
out of the junction.

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PARALLEL CIRCUIT LAWS
Law 1  Total resistance of a parallel circuit is always less than that 
of the smallest­resistance leg. This occurs because not all current 
flows through each leg or branch. With many branches, more 
current can flow from the battery.
Law 2  The voltage is the same for each leg of a parallel circuit.
NOTE: A parallel circuit drops the voltage from source voltage to zero
(ground) across the resistance in each leg of the circuit.

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