Physics 102 Homework #11
Due Noon, Tuesday, April 13, 2010
Revised, April 10: Corrected typo in figure in problem 10.
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Exam:
The second midterm exam will be next week, April 13-14. It will include material covered
from the week after the first exam through the end of this week, i.e., March 2 through
April 8. This corresponds to homework assignments 7 through 11. The topics include
thermodynamics, electric forces (electric fields, potentials, etc.), and electric circuits.
The exam will not include material from the class immediately after the first exam, February
25. This material was on homework 6. This material may be on the final exam, but it will
not be on any midterm exam.
The exam will be two hours, and the exam procedure will be nearly the same as that of
midterm #1. The only difference is increased flexibility about taking the exam in the lecture
hall. You may take the exam in the lecture hall starting any time between 8:00 am and
9:00 am on Tuesday, April 13. You may take the exam in the science library any time after
10:00 am on Tuesday, April 13, or any time the library is open on Wednesday, April 14.
The exam format will be similar to that of midterm #1. An equation sheet will be provided.
Copies will be available from the course website at least two days before the exam.
This exam includes material covered in homework #11, which is due on exam day. Because
of self-scheduling, some students will take the exam before the homework is due. To be fair
to everyone, the homework solution will not be available until the exam is over. In order to
help you check your understanding of the material on this assignment, I have given more
answers than usual at the end of the problem set.
Exams from previous years are available on the website. The following problems from old
midterm exams are on material relevant to this year’s midterm #2:
Spring 2008 Midterm #2 Problems 2, 7, 8
Spring 2008 Midterm #3 Problems 4, 5, 6, 7
Spring 2009 Midterm #2 Problems 2, 4, 5, 6, 7
There will be no recitation on exam day, Tuesday, April 13.
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Reading:
This week:
KJF §23.1-23.6, 23.8; see note below.
Next week:
Tuesday/Wednesday: Exam
Thursday: Filters (some RC circuits, some material not in text)
Following week: KJF §24.
Topic coverage in §23.
• Some material in §23.1 and §23.3 was covered last week.
• The ideas behind Kirchhoff’s laws presented in §23.2 are important, but we will rarely
if ever use the mathematical form presented in equations 23.1 and 23.2. While the
formal mathematical approach provides a useful framework for solving complicated
circuit networks, it can hide the physical understanding which we strive for.
• We are skipping §23.7 on parallel and series capacitors. The ideas are similar to
parallel and series resistors, although the details differ.
• We are skipping §23.9, which gives a physical overview of the propagation of nerve
cell impulses. This is interesting material, but we don’t have time to cover it properly.
Problems: Four problems will be selected at random from among those problems indicated
with asterisks for grading. You need not to submit solutions to the non-asterisk problems.
1. KJF Conceptual Question 23.8. (Answer at the end of the assignment.)
2. * KJF Conceptual Question 23.14. Do it two ways:
(a) Answer the following without doing numerical calculations. Briefly justify each
answer (one sentence).
i. Which resistor has the greatest current?
ii. Of the two other resistors, which has the next-greatest current?
(b) Now answer this problem a second way. Make numerical calculations, using
R1 = 30 Ω, R2 = 10 Ω, and R3 = 20 Ω and battery voltage V = 10 V.
i. What is the equivalent resistance of the three resistors?
ii. What are I1 , I2 , and I3 ?
(Partial answer at the end of the assignment.)
3. KJF Problem 23.17.
4. * KJF Problem 23.22.
Hint: The ammeter tells you that the current through the central branch of the circuit
(which includes the 2 Ω resistor) is 3 A. From the orientation of the batteries and/or
the directions of currents I1 and I2 , you can reasonably guess that this 3 A current
flows downward. Start by calculating the voltage drop across the 2 Ω resistor, then
work out what is happening in the other parts of the circuit.
5. * KJF Problem 23.24. (Partial answer at the end of the assignment.)
Hint: first re-draw the circuit to make parallel and series connections clear.
6. * KJF Problem 23.56.
7. KJF Problem 23.36. (Answer at the end of the assignment.)
8. KJF Problems 23.74 through 23.77. (Answers at the end of the assignment.)
9. * KJF Problem 23.40. (Partial answer at the end of the assignment.)
10. Consider the circuit below. Initially the capacitor is uncharged and the switch is open.
At time t = 0, the switch is closed.
(a) What is the time constant for this circuit?
(b) At t = 0, how much charge is on the capacitor?
(c) At t = 10 ms, how much charge is on the capacitor?
(d) After a long time, t → ∞, how much charge is on the capacitor?
(e) Sketch graphs of resistor voltage, VR , and capacitor voltage, VC , over time. Your
sketches should look like the ∆V plots in KJF Problem 23.74.
(Answers at the end of the assignment.)
Switch
50 Ω
100V
0.1 mF
Continued on the next page....
11. * In the circuit below, the switch has been in position “A” for a very long time.
Capacitor C2 is initially uncharged.
(a) What is the charge on capacitor 1? What is the voltage across it?
The switch is moved to position “B.” Immediately after the switch is moved....
(b) What is the charge on each capacitor?
(c) What is the voltage across each capacitor?
(d) Describe any current flow. (Where does current flow? In what direction?)
The switch remains in position “B” for a long time.
(e) What is the final charge on each capacitor?
(f) What is the final voltage across each capacitor?
Now consider a nearly identical circuit, but in which capacitor 2 has capacitance
C2 = 4.0 µF. Capacitor 1 still has capacitance C1 = 2.0 µ F. This circuit is taken
through the same series of events as described in parts (a) through (f).
(g) What is the final charge on each capacitor?
(h) What is the final voltage across each capacitor?
(Partial answer at the end of the assignment.)
50 Ω
9V
A B
C1=2.0 µF
50 Ω
C2 =2.0µF
12. KJF Problem 23.68. (Answer at the end of the assignment.)
13. * KJF Problem 23.70.
Answers to selected problems:
(1) A gets brighter, B goes out.
(2) Partial answer to (b)(ii): I2 =0.182 A, I3 =0.091 A.
(5) Partial answer: Voltage across the 4 Ω resistor is 6 V; current through it is 1.5 A.
(7) 2 ms.
(8) A, C, B, B.
(9) Partial answer: (b) 11 µC, 0.11 A.
(10) (a) 5 ms. (b) 0. (c) 8.6 mC (d) 10.0 mC (e)
(11) Partial answer: (e) Q1 = 9 µC, Q2 = 9 µC. (g) Q1 = 6 µC, Q2 = 12 µC.
(12) 36 Ω.