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Class notes for the week of September 24
th
Series connected resistors
If two components are connected ‘endtoend’,
and
there are no other components connected to their
junction, then the components are said to be connected
in series. In the example at right resistors R18 and R5
are
in series, but R4 and R6
are not
in series since there
is another component connected to their junction. The
important thing about series connected components is
that the current through both components is the same.
This permits some simplifications to be made. Consider
the circuit shown at left. R1 and
R2 are in series, and they must
carry the same current,
I
. The
voltage across R1 is
I*R1
with
the positive sign on top, while the voltage across R2 is
I*R2
also
with the positive sign toward the top of the page. If we write a
KVL equation around the loop we obtain:
(
29
2
1
2
1
0
2
1
R
R
I
V
R
I
R
I
V
R
I
R
I
V
+
=

=
=


This has the same form as Ohm’s law, except that the resistance,
R,
has been replaced
with
R1+R2.
It appears that the circuit works exactly the same as if there were a single
resistor of value 10kohm (8k for
R1
plus 2k for
R2
). We define the equivalent resistance,
R
eq
, of the series connected
R1
and
R2
as:
2
1
R
R
R
eq
+
=
It is easy to extend this idea to any number of resistors in series, so that the equivalent
resistance of
n
resistors in series is just the sum of the resistances of all
n
resistors:
∑
=
n
n
eq
R
R
Voltage divider
An especially handy series resistor circuit is the voltage divider. Its use is to produce a
scaled (or divided) voltage output from a higher voltage. You might use a resistor divider
if you need a 2Vdc reference and you have only a 5Vdc power on your board. The
voltage divider is just two resistors connected in series as shown below:
I
R
1
8 k
R
2
2 k
R
3
6 . 8 k
R
4
3 . 6 k
R
5
7 . 2 k
R
6
4 . 2 k
R
1 8
7 . 2 k
R
1 9
7 . 2 k
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View Full DocumentThe output voltage,
Vout
, is taken across
R2
.
Technically, this is not a series circuit since we have a
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 Fall '07
 Westerfield

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