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Ch. 24
For a capacitor with Q and Q:
C
=
Q
Δ
V
C
k
plates
=
±
0
A
d
In parallel,
V
=
V
n
, so
C
eq
= Σ
C
n
.
In series,
Q
=
Q
n
, so
C
eq
=
1
Σ
1
Cn
.
Δ
U
=
1
2
CV
2
=
1
2
QV
=
1
2
Q
2
C
Energy density
u
=
1
2
±
0
E
2
Ch. 25
I
=
dQ
dt
J
:=
I
A
=
nqv
d
, where J is current density, A is the
crosssectional area of the conductor, n is the particle
density, and
v
d
is drift velocity.
ρ
:=
E
J
, where
ρ
is resistivity, which represents the
material dependence of resistance
ρ
(
T
) =
ρ
0
(1 +
α
(
T

T
0
))
Corrolaries:
R
=
ρL
A
, where
V
=
EL
V
=
IR
terminal voltage:
V
=
emf

IR
int
emf

IR
int

IR
ext
= 0
P
=
IV
=
I
2
R
=
V
2
R
=
emf
*
I

I
2
R
int
0.1
Ch. 26
In series:
I
eq
=
I
n
for all n, so
R
eq
=
∑
R
n
In parallel:
V
eq
=
V
n
for all n, so
1
R
eq
=
∑
1
R
n
Kirchhoﬀ’s laws:
1.
∑
I
= 0, where I is the current into a junction.
(conservation of charge)
2.
∑
V
= 0, where V is the voltage around a closed
loop. (electrostatic force is conservative)
Do loop rule on n loops, where n is the number of
internal loops, and the loops include all the circuit
elements.
Ammeter is in series, ideally
R
= 0.
Voltmeter is in parallel, ideally
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This note was uploaded on 04/01/2008 for the course PHYSICS 260 taught by Professor Evrard during the Fall '07 term at University of Michigan.
 Fall '07
 Evrard

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