NOTES
©2008 by W.H. Freeman and Company
Capacitor Examples
C
C
2C
C
C
C
C/2
C
C
?C
?=2/3
DOCCAM 1 DEMO 5B-01
OHMS LAW BOARD
DOCCAM 1 DEMO 5B-10
TEMPERATURE DEPENDENCE OF
RESISTANCE
Electric Current
Current = charges in motion
Magnitude
rate at which net positive charges
move across a cross sectional surface
Units:
[I] = C/s = A (ampere)
Current is a scalar, signed quantity, whose
sign corresponds to the direction of motion of
net positive charges by convention
J = current density
(vector) in A/m²
Microscopic View of Electric Current in Conductor
All charges move with some velocity ve
A
random motion with high speeds (O
(106)m/s) but with a drift in a certain
direction on average if E is present
Why random
motion?
•  thermal energy
•  scattering off each
other, defects, ions,
…
Drift velocity vd is orders of magnitudes less
than the actual velocity of charges.
Current and Drift Velocity in Conductor
!
Drift velocity vd is orders of
magnitudes less than the actual velocity
of charges.
where n =carrier density
or
if ohmic
Ohm’s Law Summary
Current-Potential (I-V) characteristic of a
device may or may not obey Ohm’s Law:
or V = IR with R constant
(ohms)
Resistance
tungsten wire
gas in fluorescent tube
diode
Resistance and Resitivity for Ohmic Material
(= I/A if current
density is uniform)
resistivity
A
L
R (in) Ohms Ω
resistance
Resistance
R
Resistance
(definition)
I
V
constant R
Ohm’s Law
Temperature Dependence of Resistivity
•  Usually T0 is 293K (room temp.)
•  Usually α > 0 (ρ increases as T )
Material
ρ0 (Ωm)
α (K-1)
Ag
1.6x10-8
3.8x10-3
Cu
1.7x10-8
3.9x10-3
Si
6.4x102
-7.5x10-2
glass
1010 ~ 1014
sulfur
1015
Copper
NOTES
Electric Current and Joule Heating
electron gas
•  Free electrons in a conductor gains
kinetic energy due to an externally
applied E.
•  Scattering from the atomic ions of the
metal and other electrons quickly leads to
a steady state with a constant current I.
Transfers energy to the atoms of the solid
(to vibrate), i.e., Joule heating.
Mean drift of electrons, i.e., current
Energy in Electric Circuits
•  Steady current means a
constant amount of charge ΔQ
flows past any given cross
section during time Δt, where
I= ΔQ / Δt.
Energy lost by ΔQ is
V
=> heat
So, Power dissipation = rate of decrease of U =
EMF – Electromotive Force
•  An EMF device is a charge pump that can maintain a potential
difference across two terminals by doing work on the charges
when necessary.
Examples: battery, fuel
cell, electric generator,
solar cell, fuel cell,
thermopile, …
•  Converts energy (chemical, mechanical, solar, thermal, …)
into electrical energy.
  Within the EMF device, positive charges
are lifted from lower to higher potential.
  If work dW is required to lift charge dq,
EMF
Energy Conservation
A circuit consists of an ideal battery
(B) with emf ε, a resistor R, and two
connecting wires of negligible
resistance.
Energy
conservation
•  Ideal battery: no internal
energy dissipation
•  Real battery: internal
energy dissipation exists
Work done by battery is equal
to energy dissipated in resistor
EMF ε = terminal voltage V
dW > i2Rdt then εi > iR=V
DOCCAM 1 DEMO 5B-02
TERMINAL VOLTAGE ON A BATTERY
Resistors in Series
  The current through devices
in series is always the same.
i
R1
R2
ε
For multiple
resistors in series:
i
i
Req
ε
Internal Resistance of a Battery
Life story (ups and downs) of a charge
load
internal
resistance
terminal
voltage
NOTES
Lecture Extra Quiz 3
There are 1014 electrons entering a resistor of
resistance 1.0 Ω in 10 seconds. What is the
potential drop across the resistor?
a) 3.2 mV
b) 8.0 V
c) 2.5 V
d) 1.6 µV
e) 1.9 mV
Note: e = 1.6x10-19 C
R
I
V
Extra Lecture Quiz 3
The potential drop is 6.4mV across a resistor of
resistance 1.0Ω. How many electrons enter the
wire in 5 seconds?
a)3.2×1014
b)8.0×1015
c)2.5×1012
d)2.0×1017
e)1.6×1019
Note: e = 1.6x10-19 C
R
I
V