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Class notes #4
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
. Ohm’s law tells us
that 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:
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 10 kohm (8 k for
R1
plus 2 k for
R2
). We define the equivalent
resistance,
R
eq
, of the series connected
R1
and
R2
as:
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:
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 2 Vdc voltage reference and you have only 5 Vdc power in your circuit. A
voltage divider is just two resistors connected in series as shown below:
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This note was uploaded on 10/21/2010 for the course ESE 123 taught by Professor Westerfield during the Fall '07 term at SUNY Stony Brook.
 Fall '07
 Westerfield

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