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
0
