Exam 1 F13
Phys 1220
__________
name
Each problem is of equal value.
You can skip two problems. You cannot skip more than one of problems one to
three or more than one of problems four to six.
If you work more than the required four problems, we will count the best grades
in agreement with the above rules.
Tips for better exam grades:
Read all problems right away and ask questions as early as possible.
Make sure that you give at least a basic relevant equation or figure for each
sub-problem.
Make use of the entire exam time.
Show your work for full credit. The answer ‘42’ only earns you any credit IF
‘42’ is the right answer. We reserve points for ‘steps in between’, figures,
units, etc. If all you give us is a numeric answer you may receive only a C
grade for the problem and in some cases even less.
No credit given for illegible handwriting or flawed logic in your reasoning.
All multiple choice questions may have more than one correct answer. For
full credit, you need to mark all correct answers and mark no incorrect
answer, and, where required, you need to explain your reasoning correctly.
1.
Capacitor networks
Five plate capacitors are wired up in a network (see figure).
(all values in figure are in Farad)
a) Find the equivalent capacitance of the network.
b) For Vab = 20[V], how much charge is on each capacitor?
c)
How much energy is stored in the 1[F] capacitor?
d) If one doubles the distance between the plates of each capacitor, how
much energy is now stored in the network?
2.
Lecture Video Discussion and Lab Equipment
Recall the lecture video on the charge distribution on conductors.
a) Describe an experimental setup that would test that charges accumulate only on
the outside of conductors. Explain how the measurement is conducted:
b) Mark all correct statements about the use of ammeters, voltmeters and about
errors of measurement. Below each answer explain briefly your reasoning.
A- An ammeter can be connected in series or in parallel to the device whose
current one wants to determine.
B- A voltmeter must be connected in parallel to the device whose potential drop
one wants to determine because it has zero resistance.
C- If one wants to measure currents and potential drops across a device
simultaneously, at least one of the meters will not show the true value.
D- When one uses an ammeter or a voltmeter to measure the properties of a single
resistor there will be no systematic errors.
E- You calculate a current based on measurements of resistance and voltage drop.
The calculated value is known without error.
F- A current was measured repeatedly to be: 2A, 2.2A, 2.4A, 2A. The experimental
average is 2.15A and the experimental error is 0.3A (when rounded to one significant
digit).
3. Electrostatics, resistor networks
a) Derive the rules for calculating the equivalent resistance for pure series and pure parallel
networks. Hint: Start with how current and voltage divide up in different type networks and
apply Ohm's Law.
b) Consider the network shown below and find the equivalent resistance:
c) Find the currents through the following resistors (see figure in b):
the 6 Ohm resistor furthest to the left and each of the three resistors in the parallel
branch on the far right of the network.
d) Find the voltage across the 3 Ohm and across the 7 Ohm resistor (see figure in b).
4. Electrostatics
Consider an insulating sphere surrounded by a concentric conducting shell. The sphere has
a radius of R and the outer shell has an inner radius of 2 R and outer radius of 3 R. The
sphere carries a charge of -2q, the outer shell carries a charge of +6q.
a) Draw the E(R) graph.
Hint: Include in your drawing qualitative expressions for the steepness of the curves in
terms of Q and R and exact E and V values for each of the radii on the vertical axis.
b) Are there any equipotential lines in the range 1.5R < r < 4R? If so, what do they look like?
5. Electrostatics
Three point charges with charge -2q, -2q, and +4q are arranged as shown (see
figure). The point Q is half way between the upper –2q and P, P itself is 2m and
1.125m from the two -2q charges. The positive charge is 1.5m horizontally to the
right of P.
Hint: work in multiples of k
a)
Determine the magnitude and direction of the net electric field due to
all three charges at P.
b)
Determine the electric potential due to all three charges at Q.
c)
Mark all correct answers about the situation shown in the figure and
briefly explain your reasoning. Where appropriate use figures and
formulas to support your reasoning.
AThe magnitude of the electric field due to all three charges is larger at Q
than at P.
BThe direction of the electric field due to all three charges is the same at Q
and at P.
C-
If all distances in the figure are doubled, the potential at point Q is the same.
DIf all charges in the figure are doubled, the potential at point Q remains
the same.
EAt a point half way between the two negative charges a negative charge
would experience no Coulomb force due to these two charges.
6. Electrostatics: Electric fields due to continuous charge distributions
Consider a conducting object in the shape of half of a thin ring. A charge -Q has
been put on it (see figure).
Determine
a) the magnitude and direction of the electric field at a point P on an axis that
goes through (x=0,y=0) as shown.
b)
the magnitude and direction of the electric field at point (x=0, y=0).
Master Equations – Physics 1220
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Also from mechanics:
W = U = K, E = K + U = ½ m v2 + Uel.st.
Need to take your mind of the exam for a second? Check this out:
The Ten Commandments of Physics
1. Thou shalt read thy problem…carefully.
2. Whatsoever thou doest to one side of thy equation, do ye also to the other.
3. Thou must use thy common sense, else thou wilt have flagpoles 9,000 feet high.
4. Thou shalt ignore the teachings of false prophets to do all thy work in thy head.
5. When thou knowest not, thou shalt look it up; and if thy search still elude thee, thou shalt ask thy All-Knowing
Teacher.
6. Thou shalt master each step before putting thy heavy foot down on the next.
7. Thy correct answer does not prove that thou hast worked thy problem correctly. This argument convincest none,
least of all thy Teacher.
8. Thou shalt first see that thou hast copied thy problem correctly, before bearing false witness that the answer book
lieth.
9. Thou shalt look back even unto thy youth and remember correctly in the language of mathematics, and verily A’s
and B’s shall follow thee even unto graduation.
10. Thou shalt learn, read, write, speak, and listen thy arithmetic.
"An approximate answer to the right problem is worth a good deal more than an exact answer to
an approximate problem."
Freshmen vs seniors:
Freshman: Reads the syllabus to find out what classes he can cut.
Senior: Reads the syllabus to find out what classes he needs to attend.
Freshman: Memorizes the course material to get a good grade.
Senior: Memorizes the professor's habits to get a good grade.
Freshman: Shows up at a morning exam clean, perky, and fed.
Senior: Shows up at a morning exam in sweats with a cap on and a box of pop tarts in
hand.
The Feynman Problem Solving Algorithm:
1) Write down the problem.
2) Think very hard.
3) Write down the solution.