1. Capacitor Examples C 2C C
C/2
d/4
3d/4 a

2. Current = charges in motion
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)
J = current density (vector) in A/m²
Current is a scalar, signed quantity, whose sign corresponds to the direction of motion of net positive charges by convention

3. Microscopic View of Electric Current in ConductorA
All charges move with some velocity ve
random motion with high speeds (O(106)m/s) but with a drift in a certain direction on average if E is present
thermal energy
scattering off each other, defects, ions, …
Give the value of the Vd from textbook.
Drift velocity vd is orders of magnitudes less than the actual velocity of charges,

4. Current and Drift Velocity in Conductor
Drift velocity vd is orders of magnitudes less than the actual velocity of charges. 
where n =carrier density
Vd~0.1mm/s
In the following condition:
I = 1.0A,
copper: n ~1029atoms/m3
1mm radius wire.
Vd~0.01mm/s

5. Ohm’s Law
Current-Potential (I-V) characteristic of a device may or may not obey Ohm’s Law:
or V  IR with R constant
Resistance
(ohms)
gas in fluorescent tube
tungsten wire
diode

6. Resistance and Resitivity for Ohmic Material
resistivity
R (in )
resistance L A
J is proportional to Vd which is proportional to acceleration which is proportional to E

7. Resistance V R I
Resistance (definition)
constant R Ohm’s Law

8. b) 1.6 mA c) 3.2 A d) 1.6A e) 3.2 mA Warm up
There are 2x1014 electrons across a resistor in 10 seconds. What is the current through the resistor?
a) 3.2mA
b) 1.6 mA
c) 3.2 A
d) 1.6A
e) 3.2 mA
Note: e = 1.6x10-19 C V R I

9. Temperature Dependence of Resistivity
Usually T0 is 293K (room temp.)
Usually  > 0 (ρ increases as T )
Material
0 (m)
 (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
Demo: measure R of electron bulb when T is high and low.
Superconductivity at very low temperature

10. Electric Current and Joule Heating
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.
Hit an object with a hammer, the object become hot.

11. Energy in Electric Circuits
Steady current means a constant amount of charge Q flows past any given cross section during time t, where I= Q / t. I I a b a b ∆Q ∆Q
Energy lost by Q is
=> heat
Read 27-8 (semi-conductor) and 27-9 (superconductor)
So, Power dissipation = rate of decrease of U =

12. 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

13. Internal Resistance of a Battery
load
terminal voltage
internal resistance

14. Energy Conservation
A circuit consists of an ideal battery (B) with emf , a resistor R, and two connecting wires of negligible resistance.
Energy conservation
Work done by battery is equal to energy dissipated in resistor
Ideal battery: no internal energy dissipation
Real battery: internal energy dissipation exists
dW > i2Rdt or  > iR=V

15. b) 1.0 Ω c) 2.5 Ω d) 3.0 Ω e) 4.0 Ω Lecture quiz A
There are1014 electrons across a resistor with potential drop of 3.2mV in 10 seconds. What is the resistance of the resistor?
a) 2.0 Ω
b) 1.0 Ω
c) 2.5 Ω
d) 3.0 Ω
e) 4.0 Ω
Note: e = 1.6x10-19 C V R I

16. b)8.0 V c)2.5 V d)1.6 mV e)1.6mV Lecture quiz B
There are electrons across a resistor of resistance 1.0Ω 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 mV
e)1.6mV
Note: e = 1.6x10-19 C V R I

17. b)8.0×1015 c)2.5×1012 d)4.0x1014 e)1.6×1019 Lecture quiz C
The potential drop is 6.4mV across a resistor of resistance 1.0Ω. How many electrons enter the wire in 10 seconds?
a)3.2×1019
b)8.0×1015
c)2.5×1012
d)4.0x1014
e)1.6×1019
Note: e = 1.6x10-19 C V R I