Download Exam III from spring 2002

Exam 3
Apr. 4, 2002
Physics 212 Spring 2002
Name________________________
This 100-point exam consists of four questions with five parts each. If you cannot do one part,
move on to the next. Partial credit will be given on all parts of this exam.
This is a closed book exam. You will need a calculator. Please remember to write your name on
every page. Remember to convert to meters and kilograms.
To receive full credit, you must show all of your work or reasoning. At times, you may need to
explain your reasoning in words. When grading I look for quality thinking more than right
answers so do take the time to reason carefully. Please ask if the wording of a question is not
clear to you.
Energycap  12 CV 2
Equations:


FE ,q  qE
Force on a charge, q
P = IV
Q
V
energy in a capacitor
power
E
kq
r2
point charge
C
E

2 o
single plate
1
1
1
parallel

 ... 
R1 R2
Req
V 
kq
r
potential—point charge or
1
1
1

 ... 
C1 C2
Ceq
definition of capacitance
series
sphere
V  ED
R1 + R2 +… = Req
series
C1 +C2 +… = Ceq
parallel
uniform E-field
PEAB  qVAB definition of voltage
Constants:
KEAB  PEAB
KE  21 mv 2

q
A
 V  IR
energy conservation
o = 8.8 x 10-12 C2/Nm2
kinetic energy
k = 9 x 109 Nm2/C2
charge density—plate
e = 1.6 x 10-19 C
elementary charge
mp = 1.7 x 10-27 kg
proton mass
me = 9.1 x 10-31 kg
electron mass
Ohm’s law
1
Exam 3
Apr. 4, 2002
Physics 212 Spring 2002
Name________________________
1) [25 points total] The circuit at right has been
connected for a long time and has reached a steady
state. There are no capacitors. Point A has no
significance until part e.
15V
R1
6
R3
a) [5 points] Find the total current through the
battery. Show your reasoning. (neatly please:)
R4
2
R2
3
1.5
R5
2
point A
b) [5 points] Find the voltage across R3. Show your reasoning.
c) [5 points] Find the current through R4. Show your reasoning.
d) [5 points] Find the power dissipated by R6. Show your reasoning.
e) [5 points] If the wire is cut at point A, what happens to the voltage across R3? Does it
increase, decrease, or stay the same? You do not need a number for full credit. Show
your reasoning (or show your work).
2
R6
2
Exam 3
Apr. 4, 2002
Physics 212 Spring 2002
Name________________________
2) [25 points total] All questions below refer to the circuit at
right. Use the junction rule and the loop rule, as well as
the ideas of resistance in your reasoning.
a) [5 points] How does the brightness of bulb A compare
to the brightness of bulb E? Explain your reasoning.
E
A
B
D
F
C
b) [5 points] How does the brightness of bulb A compare to the brightness of bulb D?
Explain your reasoning.
c) [5 points] How does the brightness of bulb D compare to the brightness of bulb E?
Explain your reasoning.
d) [5 points] How does the brightness of bulb D compare to the brightness of bulb F?
Explain your reasoning.
e) [5 points] How does the brightness of bulb A compare to the brightness of bulb F?
Explain your reasoning.
3
G
Exam 3
Apr. 4, 2002
Physics 212 Spring 2002
Name________________________
3) [25 points total] The circuit at right has been
connected for a long time and has reached a steady
state. There are two capacitors.
15V
a) [5 points] Find the total current through the
battery. Show your reasoning.
R1
6
C1
R4
10F R2
2
2
C2
R5
R3
30F
2
2
b) [5 points] Find the current through R4. Show your reasoning.
c) [5 points] Find the voltage across C1 and the charge stored on C1. Show your reasoning.
d) [5 points] Find the voltage across C2 and the charge stored on C2. Show your reasoning.
e) [5 points] Now the charged capacitors are arranged as shown at right.
Find the voltage across each capacitor after the system comes to
equilibrium. Hint: The voltage across each will be the same and the
total charge stored on both together cannot change.
4
C1
R4
10F R2
2
2
C2
30F
Exam 3
Apr. 4, 2002
Physics 212 Spring 2002
Name________________________
4) [25 points total] Two capacitors are arranged as in the class handout, except that they are of
unequal capacitance. One is three times the capacitance of the other. Both arrangements are
connected to a 12V battery.
II
I
10F
12V
10F
12V
30F
30F
a) [5 points] What is the ratio of the charges on the capacitors in circuit I? Are they equal?
2:1? 3:1? 4:1? Show your reasoning.
b) [5 points] What is the ratio of the charges on the capacitors in circuit II? Are they equal?
2:1? 3:1? 4:1? Show your reasoning.
c) [7 points] Find the voltage across the 30F capacitor and the charge on the 30F
capacitor in circuit II. Show your reasoning.
d) [8 points] If circuit II is disconnected from the battery and the
charged capacitors are connected to a resistor as shown, find the total
charge that passes through the resistor and the total energy dissipated
by the resistor as the system discharges. Show your reasoning.
5
10F
10
30F