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Chapter 10
Resistors in Series and Parallel; Measuring I & V
70
10
Resistors in Series and Parallel; Measuring
I
&
V
The analysis of a circuit involves the determination of the voltage across, and the current through,
circuit elements in that circuit.
A method that I call “the method of ever simpler circuits” can be
used to simplify the analysis of many circuits that have more than one resistor.
The method
involves the replacement of a combination of resistors with a single resistor, carefully chosen so
that the replacement does not change the voltage across, nor the current through, the other circuit
elements in the circuit.
The resulting circuit is easier to analyze, and, the results of its analysis
apply to the original circuit.
Because the single carefullychosen resistor has the same effect on
the rest of the circuit as the original combination of resistors, we call the single resistor the
equivalent resistance of the combination, or, simply, the equivalent resistor.
Resistors in Series
One combination of resistors that can be replaced with a single effective resistor is a series
combination of resistors.
Two twoterminal circuit elements in a circuit are in series with each
other when one end of one is connected with one end of the other with nothing else connected to
the connection
1
.
For instance,
R
1
and
R
2
in the following circuit are in series with each other.
From our viewpoint, the right end of
R
1
is connected to the left end of
R
2
and nothing else is
connected to the point in the circuit where they are connected.
R
1
and
R
2
in the following circuit are also in series with each other:
1
Here we have described adjacent resistors that are in series.
Nonadjacent twoterminal circuit elements are also in
series with each other if each is in series with a third twoterminal circuit element.
In this definition, in addition to
an ordinary twoterminal circuit element such as a seat of EMF or a resistor, a twoterminal combination of circuit
elements is considered to be a twoterminal circuit element.
2
R
1
R
V
R
1
R
2
R
3
V
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Resistors in Series and Parallel; Measuring I & V
71
But,
R
1
and
R
2
in the following circuit are
not
in series with each other:
While it is true that the right end of
R
1
is connected to the left end of
R
2
, it is not true that
“nothing else is connected to the connection.”
Indeed, the left end of
R
3
is connected to the point
in the circuit at which
R
1
and
R
2
are connected to each other.
In implementing the method of ever simpler circuits, the plan is to replace a combination of
resistors that are in series with each other with a single, wellchosen
equivalent
resistor.
The
question is, what value must the resistance of the single resistor be in order for it to be equivalent
to the set of series resistors it replaces?
For now, we simply give you the result.
The derivation
will be provided in the next chapter.
The equivalent resistance of resistors in series is simply the sum of the resistances.
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 Fall '08
 RABE
 Physics, Current

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