Physics 4B Lecture Notes
281
Chapter 28  Circuits
Problem Set #7  due:
Ch 28  1, 9, 14, 17, 23, 38, 47, 53, 57, 66, 70, 75
Lecture Outline
1. Kirchoff's Rules
2. Resistors in Series
3. Resistors in Parallel
4. More Complex Circuits
5. Electrical Meters
6. RC Circuits
In a circuit, charges move from one place to another carrying energy.
These
charges can be thought of as buckets that carry energy around a circuit.
The
battery fills the buckets.
The buckets are emptied at various places around the
circuit, but the buckets themselves never disappear.
They return to the battery to
be refilled. These basic ideas are summarized in Kirchoff's Rules and are
applicable to even the most complicated circuits.
1.
Kirchoff's
Rules
The
Junction
Theorem:
"The current into any junction is exactly equal to the current out of the junction."
This theorem is explained by the Law of Conservation of Charge.
The
Loop
Theorem:
"The sum of all the voltage drops around any loop in a circuit must be zero."
This theorem is explained by The Law of Conservation of Energy and the fact that the electric force is
conservative.
2.
Resistors
in
Series
I
V
R
1
2
R
N
R
The loop theorem requires:
V

V
1

V
2

L

V
N
=
0
⇒
V
=
V
1
+
V
2
+
L
+
V
N
Ohm's Law says:
V
=
IR, V
1
=
I
1
R
1
, V
2
=
I
2
R
2
,
L
V
N
=
I
N
R
N
⇒
IR
=
I
1
R
1
+
I
2
R
2
+
L
+
I
N
R
N
The junction theorem means that:
I
=
I
1
=
I
2
=
L
=
I
N
⇒
IR
=
IR
1
+
IR
2
+
L
+
IR
N
⇒
R
=
R
1
+
R
2
+
L
+
R
N
R
s
=
R
i
∑
Resistors in Series
V
I
R
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Physics 4B Lecture Notes
282
3.
Resistors
in
Parallel
I
R
1
2
R
N
R
V
I
1
2
I
N
I
The junction theorem means that:
I
=
I
1
+
I
2
+
L
+
I
N
Ohm's Law says:
I
=
V
R
, I
1
=
V
1
R
1
, I
2
=
V
2
R
2
,
L
I
N
=
V
N
R
N
⇒
V
R
=
V
1
R
1
+
V
2
R
2
+
L
+
V
N
R
N
The loop theorem requires:
V

V
1
=
0,
V

V
2
=
0,
L
V

V
N
=
0
⇒
V
=
V
1
=
V
2
=
L
=
V
N
So,
V
R
=
V
R
1
+
V
R
2
+
L
+
V
R
N
⇒
1
R
=
1
R
1
+
1
R
2
+
L
+
1
R
N
Resistors in Parallel
1
R
p
=
1
R
i
∑
4.
More
Complex
Circuits
1) Circuit elements in series have the same current, but divide up a common voltage.
2) Circuit elements in parallel have the same voltage, but divide up a common current.
Many resistor circuits are just combinations of series and parallel.
They can be studied using the series
and parallel rules.
This is called "circuit reduction."
Other circuits are not combinations of series and
parallel.
These circuits have to be examined with Kirchoff's Rules.
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 Fall '09
 Staff
 Physics, Resistor, Electrical resistance, Electrical impedance

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