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V6.01 RS/BQ S’10
67
Chapter 26: DirectCurrent Circuits
analysis of a circuit can often be simplified by replacing groups of resistors by a
single
resistor of
equivalent resistance
Resistors in Series and Parallel (261)
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
V
VV
V
=
=
•
total current through set is sum of currents
through each
•
to replace by single resistor,
with equivalent resistance
a
b
R
R
R
R
R
1
2
3
4
5
a
b
R
R
R
R
R
1
2
3
4
5
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
V
IR
=
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
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68
example
:
find current
I
drawn from power supply
(having negligible internal resistance) and voltage
2
V
across
2
R
R
12
R
34
ε
•
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 the single equivalent resistor
which is
many practical resistor networks (eg. bridge
network) can
not
be reduced to simple series
parallel combinations (use Kirchhoff’s rules)
2
R
1
R
4
R
3
R
a
b
1234
R
E
+
12
34
14V
3.0 k
6.0 k
2.0 k
6.0 k
RR
=
=Ω=Ω
E
( )
( )
1234
12
34
1
2
3
4
(3)(6)
(2)(6)
k
3.5 k
36
26
R
R
R
=+=
+
=
+
Ω=
++
1234
14V
4.0 mA
3.5k
I
R
=
=
=
Ω
E
12
1
2
2k
R
=
=
=
+
1
R
2
R
3
R
4
R
b
R
E
+
2
12
(4.0mA)(2k ) 8.0V
V
IR
=
=
Ω
1
R
2
R
3
R
4
R
E
+
I
b
V6.01 RS/BQ S’10
69
junction
: a point in a circuit where 3 or more conductors meet
Kirchhoff’s Rules (262)
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
Kirchhoff’s
junction rule
•
algebraic sum of the currents
into
any junction is zero
•
follows from charge conservation and requiring that
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This note was uploaded on 08/25/2011 for the course PHYSICS II 33107 taught by Professor B.quinn during the Summer '10 term at Carnegie Mellon.
 Summer '10
 B.QUINN

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