1. Physics 122B Electricity and Magnetism
Lecture 13 (Knight: 30.6 and 30.7)
Capacitance and Capacitors
April 25, 2007
Martin Savage

2. Lecture 13 Announcements
Lecture HW #4 has been posted on the Tycho system, it is due at 10 PM tonight
11/28/2018
Physics 122B - Lecture 13

3. Combining Capacitors Parallel: Same DV, but different Qs.
Series: Same Q, but different DVs.
11/28/2018
Physics 122B - Lecture 13

4. Reminder: Combining Resistors
Conducting material that carries current across its length can form a resistor, a circuit element characterized by an electrical resistance R: R ≡ rL/A where L is the length of the conductor and A is its cross sectional area. R has units of ohms.
Multiple resistors may be combined in series, where resistances add, or in parallel, where inverse resistances add.
Rnet
Rnet I
11/28/2018
Physics 122B - Lecture 13

5. Example: A Capacitor Circuit
Find the charge and potential difference across each capacitor shown in the figure.
11/28/2018
Physics 122B - Lecture 13

6. Energy Stored in a Capacitor
11/28/2018
Physics 122B - Lecture 13

7. Example: Storing Energy in Capacitor
How much energy is stored in a 2.0 mF capacitor that has been charged to 5000 V?
What is the average power dissipation if the capacitor is discharged in 10 ms?
2.0 mF
5 kV
11/28/2018
Physics 122B - Lecture 13

8. Energy in the Electric Field
Volume of E-field
Example: d=1.0 mm, DVC=500 V
11/28/2018
Physics 122B - Lecture 13

9. Dielectric Materials*
There is a class of polarizable dielectric materials that have an important application in the construction of capacitors. In an electric field their dipoles line up, reducing the E field and potential difference and therefore increasing the capacitance:
E off
E on
11/28/2018
Physics 122B - Lecture 13

10. Electric Fields and Dielectrics
In an external field EO, neutral molecules can polarize. The induced electric field E’ produced by the dipoles will be in the opposite direction from the external field EO. Therefore, in the interior of the slab the resulting field is E = EO-E’.
The polarization of the material has the net effect of producing a sheet of positive charge on the right surface and a sheet of negative charge on the left surface, with E’ being the field made by these sheets of charge.
11/28/2018
Physics 122B - Lecture 13

11. Capacitors and Dielectrics*
If a capacitor is connected to a battery, so that it has a charge q, and then a dielectric material of dielectric constant ke is placed in the gap, the potential is unchanged but the charge becomes keq.
If a capacitor is given a charge q, and then a dielectric material of dielectric constant ke is placed in the gap, the charge q is unchanged, but the potential drops to V/ke.
11/28/2018
Physics 122B - Lecture 13

12. Conductivity and Resistivity
11/28/2018
Physics 122B - Lecture 13

13. Example: The Electric Field in a Wire
A 2.0 mm diameter aluminum wire carries a current of 800 mA.
What is the electric field strength inside the wire?
11/28/2018
Physics 122B - Lecture 13

14. Example: Mean Time Between Collisions
What is the mean time between collisions for electrons in copper, for which the electron density is 8.5 x 1028 electrons per cubic meter?
11/28/2018
Physics 122B - Lecture 13

15. Potential and Current (1)
11/28/2018
Physics 122B - Lecture 13

16. Potential and Current (2)
Assuming uniform J across A
11/28/2018
Physics 122B - Lecture 13

17. Resistors and Resistance
Conducting material that carries current across its length can form a resistor, a circuit element characterized by an electrical resistance R defined by: R ≡ rL/A where L is the length of the conductor and A is its cross sectional area. R has units of ohms (W = V/A).
Multiple resistors may be combined in series, where resistances add, or in parallel, where inverse resistances add.
Rnet
Rnet I
11/28/2018
Physics 122B - Lecture 13

18. Question What is the relation of the currents at the points shown?
(a) Ia=Ib=Ic=Id; (b) Ia=Ib>Ic=Id; (c) Ia>Ib>Ic>Id; (d) Ia>Ib>Ic=Id;
11/28/2018
Physics 122B - Lecture 13

19. Resistors and Ohm’s Law
11/28/2018
Physics 122B - Lecture 13

20. Example: The Current in a Wire
What is the current in a 1.0 mm diameter 10.0 cm long copper wire that is attached to the terminals of a 1.5 V battery.
11/28/2018
Physics 122B - Lecture 13

21. Ohmic and Non-ohmic Materials
Despite its name, Ohm’s Law is not a law of Nature (in the sense of Newton’s Laws). It is a rule about the approximately linear potential-current behavior of some materials under some circumstances.
Important non-ohmic devices:
Batteries, where DV=E is determined by chemical reactions independent of I;
Semiconductors, where I vs. DV can be very nonlinear;
Light bulbs, where heating changes R;
Capacitors, where the relation between I and DV differs from that of a resistor.
11/28/2018
Physics 122B - Lecture 13

22. The Ideal Wire Model
In considering electric circuits, we will make the following assumptions:
Wires have very small resistance, so that we can take Rwire=0 and DVwire=0 in circuits. Any wire connections are ideal.
Resistors are poor conductors with constant resistance values from 10 to 108 W.
Insulators are ideal non-conductors, with R=∞ and I=0 through the insulator.
11/28/2018
Physics 122B - Lecture 13

23. Circuit Elements & Diagrams
These are some of the symbols we will use to represent objects in circuit diagrams.
Other symbols: inductance, transformer, diode, transistor, etc.
11/28/2018
Physics 122B - Lecture 13

24. Circuit Diagram Actual Circuit Circuit Diagram 11/28/2018
Physics 122B - Lecture 13

25. Circuit Diagrams
11/28/2018
Physics 122B - Lecture 13

26. Anatomy of a Light Bulb
11/28/2018
Physics 122B - Lecture 13

27. Question (u) (v) (w) (x)
Which of these diagrams show the same circuit?
(a) All show different circuits;
(b) (u) and (v);
(c) (u), (v), and (w);
(d) (u), (v), and (x);
(e) All show the same circuit.
11/28/2018
Physics 122B - Lecture 13

28. End of Lecture 13
Before the next lecture, read Knight, sections 30.5 and 31.4.
Lecture HW #4 has been posted on the Tycho system. and is due at 10 PM tonight.
11/28/2018
Physics 122B - Lecture 13