1. Last time… Equipotential lines Capacitance and capacitors
Thur. Oct. 9, 2007
Physics 208 Lecture 12

2. Parallel plate capacitor-Q
Geometrical factor determined from electric fields +Q
Energy stored in parallel-plate capacitor
Energy density d
Thur. Oct. 9, 2007
Physics 208 Lecture 12

3. Quick Quiz
An isolated parallel plate capacitor has charge Q and potential V. The plates are pulled apart. Which describes the situation afterwards? +Q -Q + - d
pull
A) Charge Q has decreased
B) Capacitance C has increased
C) Electric field E has increased
D) Voltage difference V between plates has increased
E) None of these
Cap. isolated  Q constant
C = e0A/d  C decreases
E = (Q/A)/e0  E constant
V= Ed  V increases
Thur. Oct. 9, 2007
Physics 208 Lecture 12

4. Quick Quiz
An isolated parallel plate capacitor has a charge q. The plates are then pulled further apart. What happens to the energy stored in the capacitor? +q -q + - d
pull
1) Increases
2) Decreases
3) Stays the same
Thur. Oct. 9, 2007
Physics 208 Lecture 12

5. Different geometries of capacitors+Q +Q -Q d A -Q L
Spherical capacitor
Cylindrical capacitor
Parallel plate capacitor
Thur. Oct. 9, 2007
Physics 208 Lecture 12

6. Combining Capacitors — Parallel
Connect capacitors together with metal wire C1 C2
Ceq
“Equivalent” capacitor
Both have same V
Potential difference V
Need different charge
Total charge
Q on each is same
Thur. Oct. 9, 2007
Physics 208 Lecture 12

7. Combining Capacitors — SeriesVA VA C1 Q Q
Ceq Vm -Q Q C2 -Q -Q VB VB
Thur. Oct. 9, 2007
Physics 208 Lecture 12

8. Thur. Oct. 9, 2007
Physics 208 Lecture 12

9. Current in a wire: not electrostatic equilibrium
Battery produces E-field in wire
Contract this with electrostatic equiibriium: charges not moving, all constant potential.
Charge moves in response to E-field
Thur. Oct. 9, 2007
Physics 208 Lecture 12

10. Electric Current Depends on sign of charge:
Electric current = I = amount of charge per unit time flowing through a plane perpendicular to charge motion
SI unit: ampere 1 A = 1 C / s
Depends on sign of charge:
+ charge particles: current in direction of particle motion is positive
- charge particles: current in direction of particle motion is negative
Thur. Oct. 9, 2007
Physics 208 Lecture 12

11. Quick Quiz
An infinite number of positively charged particles are uniformly distributed throughout an otherwise empty infinite space. A spatially uniform positive electric field is applied. The current due to the charge motion
A. increases with time
B. decreases with time
C. is constant in time
D. Depends on field
Constant force qE
Produces constant accel. qE/m
Velocity increases v(t)=qEt/m
Charge / time crossing plane increases with time
Say that charges move in response to an electric field (potential difference).
Thur. Oct. 9, 2007
Physics 208 Lecture 12

12. But experiment says… Current constant in time Proportional to voltage
R = resistance (unit Ohm = )
Also written
J = current density = I / (cross-section area)
 = resistivity = R x (cross-section area) / (length)
Resistivity is independent of shape
Ask how can this be. Constant voltage produces constant electric field - > acceleration.
Thur. Oct. 9, 2007
Physics 208 Lecture 12

13. Charge motion with collisions
Wire not empty space, has various fixed objects.
Charge carriers accelerate, then collide.
After collision, charged particle reaccelerates.
Result: average “drift” velocity vd
Do Knutson demo of rubber ball in array of nails.
Thur. Oct. 9, 2007
Physics 208 Lecture 12

14. Current and drift velocity
This average velocity called drift velocity
This drift leads to a current
Current density J
Conductivity
Electric field
Thur. Oct. 9, 2007
Physics 208 Lecture 12

15. What about Ohm’s law? Current density proportional to electric field
Current proportional to current density through geometrical factor
Electric field proportional to electric potential through geometrical factor
Thur. Oct. 9, 2007
Physics 208 Lecture 12

16. Resistivity Resistivity SI units Ω-m Independent of sample geometry
Do temperature dependent resistance
Thur. Oct. 9, 2007
Physics 208 Lecture 12

17. Resistors Circuits Physical layout Schematic layout Thur. Oct. 9, 2007
Make point here that energy is dissipated in the resistor due to collisions. Say it is dissipated as heat in resistors, light in light bulbs. Will see later that it is not directly proportional to current, but more current -> more dissipation -> hotter resistor or brighter light. Need this for the demos and next quizzes.
Schematic layout
Thur. Oct. 9, 2007
Physics 208 Lecture 12

18. Quick Quiz Which bulb is brighter? A B Both the same
Say that light bulbs are like resistors, and that more current flowing through the bulb makes the bulb brighter.
Current through each must be same
Conservation of current (Kirchoff’s current law)
Charge that goes in must come out
Thur. Oct. 9, 2007
Physics 208 Lecture 12

19. Current conservation I2 Iin I1 I3 I1=I2+I3 I1 I3 Iout I2 Iout = Iin
Thur. Oct. 9, 2007
Physics 208 Lecture 12

20. Quick Quiz B brighter than A B dimmer than A Both the same
How does brightness of bulb B compare to that of A?
B brighter than A
B dimmer than A
Both the same
Say that light bulbs are like resistors, and that more current flowing through the bulb makes the bulb brighter.
Battery maintain constant potential difference
Extra bulb makes extra resistance -> less current
Thur. Oct. 9, 2007
Physics 208 Lecture 12