PUSHING ELECTRONS
by Steve Bodofsky
The Rules of Parallel Circuits
I
n the last issue of GEARS, we
looked at series circuits. Not a
really common circuit in automotive use, but an important learning experience because series circuits help us
understand how to recognize unwanted
resistance in a circuit.
In this issue we’re going to move
to one of the most common types of
circuit used in automotive applications:
the parallel circuit.
A parallel circuit consists of two
main parts: the common circuit components and the individual legs of the
circuit (figure 1). The common components include the power and ground
sources; the legs are the individual circuits that receive power and ground
from the common components. Each
individual circuit receives full power
and ground from the source, and each
leg of the circuit operates separately
from the others.
Why are parallel circuits more
common than simple or series circuits?
Unlike simple circuits, parallel circuits
allow a single power source and ground
to operate multiple components. And
unlike series circuits, which also control
multiple components, if one component
fails in a parallel circuit, the other components continue to operate normally.
So, in a parallel circuit, it’s possible for
one bulb to burn out and the rest continue to light.
Probably the most common instance
of a parallel circuit — at least to GEARS
readers — is the transmission solenoid
circuit. All of the solenoids share a
power source or ground, regardless of
whether they’re power controlled or
ground controlled. What makes this
type of parallel circuit a little harder to
recognize is that each of the controlled
legs in the circuit is controlled individually through the transmission computer.
But the computer is actually nothing
more than a set of individual switches for
each leg of the circuit, energizing each
leg separately at the proper moment. In
every case, the transmission solenoids
still share a common feed and ground
source, making them a parallel circuit.
34
34-38PushElectrons.indd 34
The thing to remember about paralAs a distinct simple circuit, each
lel circuits is that they’re actually more
leg has to obey Ohm’s Law, which tells
like a series of individual simple cirus that current flow is based directly on
cuits. Each leg of the circuit obeys the
the circuit resistance. Which means this
rules of a simple circuit. What makes
rule has to be true.
a parallel circuit different is how curRule 4: The total current flow
rent flows in the parts of the circuit that
through the circuit is constant through
those individual circuits share.
the common components of the circuit,
Let’s look at the rules governing
and depends on the total resistance of
parallel circuits, and see how they affect
the circuit. A quick check using a curnormal diagnosis.
rent clamp proves that current flow is
Rule 1: Each leg of the circuit
indeed constant through the common
receives the same level of voltage and
components in the circuit (figure 6).
ground. A simple voltage check at the
And Ohm’s Law tells us that the
positive and negative sides of each leg
total resistance of any circuit determines
of the circuit proves this (figures 2 and
the total current flow. Where the fun
3). In this case, each leg of the circuit
comes in is how we determine the total
is powered directly by system voltage
resistance of the circuit… but we’ll be
and system ground, so the voltage and
covering that in the next rule.
ground levels for each leg are equal to
Rule 5: The total resistance of a
system voltage and ground.
parallel circuit is equal to the reciproAny drop below system voltage
cal of the sum of the reciprocals of the
— or rise above system ground level
individual resistances in each leg of the
— indicates unwanted resistance in the
circuit.
circuit.
Rule 2: Current has more
than one path it can take through
the circuit. This should be obvious simply by looking at the
circuit. What’s important about
this rule is that it’s the reason
that one leg of the circuit can
continue to operate if one of the
other legs burns out.
We can prove this fairly
easily, simply by loosening one Figure 1: A parallel circuit consists of two main
of the bulbs (figure 4). As you parts: the common circuit components, and the
individual legs of the circuit.
can see, the loosened bulb is
out, but the other remains lit.
Rule 3: The current that
flows through each leg of the
circuit is constant throughout
that leg of the circuit, and that
current level depends on the
resistance in that leg. Remember
what we said earlier about each
individual leg acting as its own
simple circuit? Each leg has a
power feed, ground, conductors
Figure 2: A simple voltage check proves that
and a load. And a simple check each leg of a parallel circuit receives the same
shows that current is indeed voltage as every other leg. Any drop in voltage
constant on either side of the leg would indicate unwanted resistance in that leg
of the circuit.
of the circuit (figure 5).
GEARS November / December 2005
11/8/05 3:19:44 PM
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Parallel Circuits
Well, that sounds simple enough,
doesn’t it? Okay, maybe not… at least
not for those of us who had a tendency
to doze off during math class. But let’s
see what “the reciprocal of the sum of
the reciprocals” means:
• A reciprocal of any whole number
is 1 over that number. So the reciprocal of 2 is ½. The reciprocal of
4 is ¼, and so on. In the case of a Figure 3: Once again, a voltage check proves
fraction, you simply invert the frac- that each leg of the parallel circuit receives the
tion; so the reciprocal of ½ is 2/1, same level of ground as the other legs. Any
or 2.
voltage on the ground side of one of the legs
• A sum is the total of any numbers would indicate unwanted voltage in
that leg of the circuit.
being added together.
So the sum of the reciprocals is
simply:
+
+
…where R1 is the first resistor, R2
is the second resistor, and so on.
And that leads us to the rest of the
formula: the reciprocal of the sum of the
reciprocals. Which looks like this:
Figure 4: The big advantage to a parallel circuit
is that even if one of the legs burns out or
If that doesn’t look complicated opens, the rest continue to work normally.
+
+
enough, remember, to add fractions, you
must first have common denominators;
that is, the bottom number of each fraction — the denominator — must be the
same for all of the fractions. Then you
add just the numerator (the top number);
the denominator remains the same.
Whew! That’s a lot of math to deal
with, just to work out total circuit resistance. Fortunately there’s an easier way
to deal with the total resistance of a par- Figure 5: A quick check shows that current is
allel circuit, and once again, it depends indeed constant through the leg of the circuit.
And, as Ohm’s Law proves, that current level
on being familiar with Ohm’s Law:
Remember what we said in Rule 3 will depend on the applied voltage and the
resistance in that leg.
about each leg being like a simple circuit? That can help you determine total
circuit current flow; here’s how:
• Calculate the current flow for each
leg, based on the applied voltage
and resistance as determined by
Ohm’s Law.
• Add the current flow for each individual leg, to get the total circuit
current flow for the circuit.
• Use Ohm’s Law again to determine
total circuit resistance, based on Figure 6: Once again, a simple current flow
total current flow.
measurement shows that current is indeed
For example, say we have a parallel constant in all of the common areas of the
parallel circuit. And that current level will
circuit with three legs. The individual
depend on the applied voltage and the total
resistances are:
circuit resistance, according to Ohm’s Law.
36
34-38PushElectrons.indd 36
R1 = 3 Ohms
R2 = 4 Ohms
R3 = 6 Ohms
We’ll assume an applied voltage of
12 volts, mainly because I’m too lazy
to use a more realistic value. Based on
Ohm’s Law, the current flow for each leg
of the circuit is:
R1 = 4 Amps
R2 = 3 Amps
R3 = 2 Amps
So the total circuit current flow
through the parallel circuit is 9 amps.
Plugging that into Ohm’s Law, we
get 12 volts divided by 9 amps, for a
total circuit resistance of 1 1/3 ohms.
If we use those same resistances in
the original, more complicated formula,
we get this:
+
+
+
+
…which still gives us 1 1/3 ohms.
But using the sum of the amperage readings is easier to work with.
There are a couple special situations
you might also want to keep in mind
when working out total circuit resistance
for a parallel circuit.
When there are only two resistances
in the circuit:
+
And if all of the resistances in the
circuit are equal, there’s another special
formula for calculating total circuit resistance:
Rule 6: The total resistance of a
parallel circuit will always be less than
the resistance in any of the individual
legs of the circuit. Which means, in the
example we just used, the total circuit
resistance will be less than 2 ohms: the
lowest resistance in the circuit. And it was
1 1/3 ohms, which is indeed lower than
the lowest resistance.
This is an important point to remember, because it means that adding a leg
to a parallel circuit can have a dramatic
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Parallel Circuits
effect on the total circuit resistance.
Some of you are probably old enough
to remember when computer systems
were first introduced to the automotive
market. Back then the manufacturers
were quick to announce that you’d have
to give up your old analog meter, and get
a digital meter with at least 10 megohms
impedance. Ever wonder why?
It’s because, when you connect a
voltmeter to measure circuit voltage,
you’re creating a parallel circuit between
that circuit and the meter. If the meter’s
resistance is too low, its additional circuitry will alter the total resistance of the
circuit. That can change the measured
voltage, and affect your diagnosis.
High impedance is the same as high
resistance; and by using a high impedance meter, you limit the effect of the
additional path of electricity through the
circuit, so your readings won’t change
much: An important consideration when
testing those computer circuits.
Rule 7: The voltage drop will be
equal in each leg of the circuit. We’ve
already shown that each leg will receive
system voltage and ground. And since
each leg works like a simple circuit,
all of the voltage will be used by the
resistance in that circuit. So the voltage
drop for each leg of the circuit should
be equal; if there’s any difference in the
voltage drop in any of the legs of the circuit, it indicates an unwanted resistance
somewhere in that leg of the circuit.
Rule 8: A parallel circuit is sometime called a Current Divider Network.
That’s because the total current flow
is divided between the individual legs
of the circuit; something we discussed
briefly in rule 3.
That’s all for this issue; next time
we’ll look at series/parallel circuits, a
hybrid that combines the features of
both a series circuit and a parallel circuit. Until then, keep on pushing those
electrons!
TEST
1. Tech A says the common components in a parallel circuit are
the resistances.
Tech B says the individual legs
of a parallel circuit provide power
and ground for the circuit.
Who’s right?
A. A only.
B. B only.
C. Both A and B.
D. Neither A nor B.
2. The most familiar use of a
parallel circuit — at least to
GEARS readers — is:
A. Transmission solenoids
B. Christmas tree lights
C. Hanukkah menorah
D. Malfunction Indicator Lamp
(MIL)
D. The reciprocal of the difference of the reciprocals of the
individual resistances.
5. A simpler way to calculate the
total circuit resistance in any
parallel circuit is:
A. multiply the resistances and
divide by the sum1 of the
resistances.
B. calculate current flow for each
leg; add the currents; and use
Ohm’s Law to calculate the total
resistance.
C. divide the value of one resistance by the number of resistances.
D. divide the sum of the resistances by the product1 of the
resistances.
3. Tech A says each leg of a
parallel circuit should receive
the same levels of power and
ground.
Tech B says the voltage drop
should be identical for each leg
of the circuit.
Who’s right?
A. A only.
B. B only.
C. Both A and B.
D. Neither A nor B
6. If there are only two legs in a
parallel circuit, you can calculate total circuit resistance by:
A. dividing the sum of the resistances by the difference2.
B. dividing the product of the
resistances by the sum.
C. dividing the quotient1 of the
resistances by the product.
D. multiplying the sum of the
resistances by the product.
4. The formula for measuring total
circuit resistance in a parallel
circuit is:
A. E = I x R
B. E = MC2
C. The reciprocal of the sum of
the reciprocals of the individual resistances.
7. If all the legs in a parallel circuit
have the same resistance, you
can calculate the total resistance by:
A. dividing the number of legs in
the circuit by the resistance of
one leg.
B. multiplying the number of legs
by the resistance of one leg.
C. multiplying the resistance of
one leg by 3.
D. dividing the resistance of one
leg by the number of legs in
the circuit.
8. The total resistance of a parallel circuit will always be:
A. equal to the leg with the lowest resistance.
B. equal to the leg with the highest resistance.
C. lower than the leg with the
lowest resistance.
D. higher than the leg with the
highest resistance.
9. The main reason for using a
high impedance meter when
measuring computer circuits
is:
A. to prevent the meter from
affecting total circuit resistance.
B. to provide a more accurate
display than an analog meter.
C. to provide a greater resolution
of the measurement.
D. to enable companies to sell
more expensive meters.
10. Technician A says another
name for a series circuit is a
Voltage Divider Network.
Technician B says another name
for a parallel circuit is a Current
Divider Network.
Who’s right?
A. A only.
B. B only.
C. Both A and B.
D. Neither A nor B.
Answers: 1. B, 2. A, 3. A, 4. C, 5. B, 6. B, 7. D, 8. C, 9. A, 10. C
38
34-38PushElectrons.indd 38
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