53
Chapter 26: DirectCurrent Circuits
Resistors in Series and Parallel (261)
±
analysis of a circuit can often be simplified by replacing groups of resistors by a
single
resistor of
equivalent resistance
±
For resistors in
series
•
same current flows through
each resistor
123
II
I
I
===
•
total voltage across set is
sum of voltages across each
•
to replace by single resistor,
with equivalent resistance
±
For resistors in
parallel
•
same voltage across each
resistor
ab
VV
V
V
==
=
•
total current through set is sum
of currents through each
•
to replace by single resistor,
with equivalent resistance
1
R
V
b
I
3
R
2
R
I
a
b
V
a
V
x position
()
11
2 2
33
1
2
3
ab
V
V
I
RI
R
I
R
I
RR
R
=+
+
+
=
+
+
eq
ab
VI
R
=
eq
1
2
(series)
R
+
"
3
12
111
ab
I
I
V
R
V
R
+
+
⎛⎞
+
⎜⎟
⎝⎠
eq
ab
V
I
R
=
eq
1
2
(parallel) "reciprocal sum"
1
R
+
"
1
R
V
b
I
3
R
2
R
I
a
b
V
a
V
1
I
2
I
3
I
y position
Path
of
least resistance
carries
most current
0
R
≡
±²³ ²´
in wires
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±
example
:
find current
I
drawn from power supply
(having negligible internal resistance) and voltage
2
V
across
2
R
•
equivalent resistance
•
current drawn is
•
voltage
2
V
across
2
R
is the same as across
1
R
, which is the same as the voltage across a single equivalent resistor
which is
±
many practical resistor networks cannot be
reduced to simple seriesparallel combinations
•
bridge circuit shown is one example
•
use of Kirchhoff’s rules
Kirchhoff’s Rules (262)
±
junction
: a point in a circuit where 3 or more
conductors meet
±
loop
:
any closed conducting path
±
currents in arbitrarily complex circuit can be found from
N
linear equations in
N
unknowns using
Kirchhoff’s two rules
1234
R
E
+
12
34
14V
3.0 k
6.0 k
2.0 k
6.0 k
RR
==
Ω
=
Ω
=Ω=Ω
E
( ) ( )
1234
1
2
3
4
(3)(6)
(2)(6)
k3
.
5
k
36
26
R
R
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 Spring '07
 Morningstar
 Physics, Current, Resistance, Resistor, Electrical resistance, Kirchhoff, R1 R2 R3

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