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```PHYS 212 – MT2
Spring 2013
Sample 2
Question 1
Suppose a region of space has a uniform electric field directed
downwards as shown. Three points are labeled A, B, and C.
Points B and C are on the same horizontal line. Which statement
is correct
A
A. The voltage at all three locations is the same
B. The voltage at points B and C are equal, and the voltage
at point B is higher than the voltage at point A
B
C
C. The voltage at points B and C are equal and the voltage
at point B is lower than the voltage at point A
D. The voltage at point A is the highest, the voltage at point
C is the second highest, and the voltage at point B is the lowest
E. None of the above
Question 2
You have two identical resistors. If you connect just one of them to a battery, there is 10 W of
heat dissipated in the resistor. If you connect both of them in parallel to the same battery, what
total heat will be dissipated?
A.
B.
C.
D.
E.
2W
5W
10 W
20 W
100 W
Page 1 of 10
PHYS 212 – MT2
Spring 2013
Sample 2
The following three questions refer to this situation.
Two capacitors, labeled 1 and 2, are attached in
parallel to a battery of constant voltage V as shown.
Capacitor 1 has a charge Q (meaning +Q on one
plate, –Q on the other) and capacitor 2 has a charge
of 3Q.
V
C1 , Q
C2 , 3Q
Question 3
Which capacitor has the smallest capacitance?
A.
B.
C.
D.
capacitor 1
capacitor 2
Both have the same capacitance.
impossible to tell from the information given
Question 4
Suppose the battery has variable voltage. If the voltage of the battery is doubled, how much
charge flows through the battery as its voltage is increased from V to 2V?
A.
B.
C.
D.
E.
zero charge
4Q
3Q
5Q
6Q
Question 5
By what factor does the energy stored in the two capacitors together increase, when the battery
voltage is doubled from V to 2V?
A.
B.
C.
D.
E.
½ (stored energy halves)
one (no increase in energy stored)
two (stored energy doubles)
None of these.
Page 2 of 10
PHYS 212 – MT2
Spring 2013
Sample 2
Question 6
In the circuit shown, the potential at B is defined to be 0 V. What is the potential at A?
A.
B.
C.
D.
E.
40 V
–40 V
50 V
80 V
20 V
Question 7
The resistors and batteries in the circuit below are all identical. Which circuit(s) have the least
power delivered to it/them?
A.
B.
C.
D.
E.
Circuit 1
Circuit 2
Circuit 3
Circuit 1 = Circuit 2
Circuit 1 = Circuit 3
Question 8
An electron (charge q = –e) is released from rest at point in empty space some distance from a
carbon ion, which has charge q = +6e. The electron is initially at a point where the voltage due
to the positively charged carbon ion is 0.50 V. Some time after release, the electron is at point
where the voltage due to the carbon ion is 1.50V. At that later time, the kinetic energy of the
electron is..
A.
B.
C.
D.
E.
6.0 eV
1.6  10–19 eV
2.0 eV
1.0 eV
None of these.
Page 3 of 10
PHYS 212 – MT2
Spring 2013
Sample 2
Question 9
The figure shows a spherical capacitor in which a conducting
sphere (labeled I) shares the same center as a conducting spherical
shell (labeled III). There is an air gap (labeled II) between the
conductors. The sphere has a total charge of +Q and the spherical
shell has a total charge of –Q. Which of the following statements
is FALSE?
A.
B.
C.
D.
E.
The electric field in region IV (outside the capacitor) is 0.
The electric field within the metallic shell (region III) is 0.
The charge on the outer surface of the shell is 0.
The electric field in region II (empty space between the two capacitor plates) is 0.
The electric field in region I (within the core sphere) is 0.
Question 10
Two parallel-plate capacitors with different capacitance but the same plate separation are
connected in series to a battery. Both capacitors are filled with air. The quantity that is the same
for both capacitors when they are fully charged is:
A.
B.
C.
D.
E.
potential difference.
stored energy.
energy density.
electric field between the plates.
charge on the positive plate.
Question 11
A uniform electric field E of magnitude 6,000 V/m exists in a region of space as shown. What is
the magnitude of the electric potential difference between points X and Y?
A.
B.
C.
D.
E.
0V
1800 V
2400 V
3000 V
4200 V
Page 4 of 10
PHYS 212 – MT2
Spring 2013
Sample 2
Question 12
A charged rod with total positive charge Q uniformly distributed along its length is positioned as
shown. The point A is located a distance r below the center of the rod. (It is a distance L from the
two ENDS of the rod) What can you conclude about the electric potential VA at point A?
A.
VA  kQ
r
B.
VA  kQ
r
C.
kQ
D.
VA  kQ
L
E.
VA  kQ
L
r
 VA  kQ
r
L
L
L
A
Question 13
The capacitance of each of the four capacitors shown is 500 F. The voltmeter reads 1000 V.
The magnitude of the charge, in coulombs, on each capacitor plate is:
A.
B.
C.
D.
E.
0.2 C
0.25 C
0.5 C
20 C
50 C
Page 5 of 10
PHYS 212 – MT2
Spring 2013
Sample 2
Question 14
Ariella connects two light bulbs in parallel across a real battery (i.e. the battery has some internal
resistance). He adds a third bulb to the circuit, also connecting it in parallel. What happens to the
current flowing through the original two bulbs?
A.
B.
C.
D.
E.
It stays the same.
It increases.
It decreases.
We need to know the value of the internal resistance to answer this.
We need to know more about the resistances of the bulbs to answer this.
Question 15
Two pairs of hollow, spherical conducting shells are connected with wires and switches. The
system AB (where A and B are far apart) is extremely far from system CD. In both systems the
large shells have four times the radius of the small shells. Before the switches are closed each
pair has a charge of +20 nC on the small shell (A,C) and +60 nC on the large shell (B,D)
A
(+20 nC)
B
(+60 nC)
C
(+20 nC)
D
(+60 nC)
When the switches are closed, charge is free to flow along the conducting wires connecting the
spherical shells. Rank the electric charge on the shells A-D after the switches are closed.
A.
B.
C.
D.
E.
QA = QB = QC = QD (the electric charge is the same for all four shells)
QC < QA < QB < QD
QA = QC < QB < QD
QC < QA = QB < QD
The ranking of the electric charge cannot be determined
Page 6 of 10
PHYS 212 – MT2
Spring 2013
Sample 2
Question 16
Consider a thin, straight rod of length L located on the positive x-axis with its left end at x = 0.
A charge Q is uniformly distributed over the rod. Which of the expressions below gives the
magnitude of the electric potential at point P located at x = L + Y on a line that is collinear with
the rod?
L
A.
kQ
dx

L 0 L  x Y 
B.
kQ
dx

L 0  x  L 2
C.
kQ
dx

L 0  x  Y 2
D.
kQ
dx

L 0 x Y 
E.
kQ
dx

L 0 x  L Y 
L
L
L
L
Page 7 of 10
PHYS 212 – MT2
Spring 2013
Sample 2
Question 17
The figure below shows the potential due to two infinite sheets of charge with
charge per unit area 1 and 2 . From examining this plot we can deduce that
A.
B.
C.
D.
E.
F.
1 and 2 have the same sign, and |1| > |2|
1 and 2 have the same sign, and |1| = |2|
1 and 2 have the same sign, and |1| < |2|
1 and 2 have opposite signs, and |1| > |2|
1 and 2 have opposite signs, and |1| = |2|
1 and 2 have opposite signs, and |1| < |2|
Page 8 of 10
PHYS 212 – MT2
Spring 2013
Question 18
The voltage between points a and b in the circuit
shown is measured with an ideal voltmeter. What
does the voltmeter read? (Hint: Recall that an
ideal voltmeter has infinite internal resistance.)
A.
B.
C.
D.
E.
Sample 2
R
R
V
a
R
V/4
V/3
V/2
V
zero
b
Question 19
You build a spherically symmetric charge distribution using only charged and neutral conductors
(no insulators, no infinitesimally thin “charge sheets” or infinitely thick slabs; just solid and
hollow spherical conductors are allowed). You measure the following potential as a function of
V
0
0
a
b
r
Based on the above information and plot, what can you say for certainty about the situation:
A.
B.
C.
D.
E.
The central conductor is solid (i.e. there is conducting material at r = 0)
There is non-zero net charge in the system
There is zero charge density at r = b
You made a mistake in either measuring or plotting the potential
None of the above
Page 9 of 10
PHYS 212 – MT2
Spring 2013
Question 20
A parallel plate capacitor has a charge-potential difference relationship as
plotted in the solid line at right. It is connected to a battery and charged
so that its state is indicated by the big blue dot.
With the battery still connected, you do positive work on the plates of the
capacitor in order to modify its charge-potential difference relationship to
one of the two dashed lines. At which, if any, of the 4 labeled states does
the capacitor end up?
A.
B.
C.
D.
E.
Sample 2
q
B
A
D
C
V
A
B
C
D
None of the above
Page 10 of 10
```
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