Download PH2200 Practice Exam II Summer 2004

PH2200 Practice Exam II
Summer 2004
Instructions
1. Write your name and student identification number on the answer sheet.
2. This a ninety minute exam.
3. Please cover your answer sheet at all times.
4. This is a closed book exam. You may use the PH2200 formula sheet that is included with the exam.
5. Equations may not be stored in calculators, nor may calculators be exchanged.
6. Record your answers in the form A, B, C, etc, on the answer sheet.
7. This exam consists of 10 concept questions worth five points each and five problems having a total of 20 parts.
The problem parts are equally weighted: each is worth five points. The total number of points on the exam is 150.
8. If you have any questions during the exam, please raise your hand and wait for assistance.
PH2200 Practice Exam II
Summer 2004
Concept Questions: Each question has a single correct answer and is worth five points.
1. The electric potential inside a charged solid spherical conductor in equilibrium
(A)
(B)
(C)
(D)
(E)
is always zero.
is constant and equal to its value at the surface.
decreases from its value at the surface to a value of zero at the center.
increases from its value at the surface to a value at the center that is a multiple of the potential at the surface.
is always positive in sign, independent of the sign of the charge on the surface.
2. A circular insulating ring is split into two semi-circles. Positive charge +Q
is uniformly distributed on the top half, and negative charge -Q is uniformly
distributed on the bottom half. The radius of the ring is R. Assuming the
electric potential at infinity is zero, the electric potential at point P, the center
of the ring is
+Q
R
(A) 0.
(B) Q / 4 o R .
(C) 2Q / 4 o R .
P
(D) Q / 4 o R2 .
-Q
(E) Q / 4 o R .
2
3. A parallel plate capacitor of capacitance C o has plates with area A and separation d between them. When connected
to a battery of voltage Vo , the capacitor has charge of magnitude Qo on its plates. The capacitor is then disconnected
from the battery, and the space between the plates is filled with a material having a dielectric constant equal to 3.
After the dielectric is added, the magnitudes of the charge on the plates and the potential difference between them are
(A) Qo , Vo .
1
1
(B) Qo , Vo .
3
3
1
(C) Qo , Vo .
3
(D) Qo , 3Vo .
(E) 3Qo , 3Vo .
4. Three capacitors have capacitances of C1 , C2 and C3 . The equivalent capacitance of the three capacitors connected
in series is
(A) Ceq  C1  C2  C3 .
1
1
1
.


C1 C2 C3
CC C C CC
(C) Ceq  1 2  2 3  1 3 .
C3
C1
C2
C
C
C
(D) Ceq  1  2  3 .
C2C3 C1C3 C1C2
C1C2C3
(E) Ceq 
.
C1C2  C2C3  C1C3
(B) Ceq 
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PH2200 Practice Exam II
Summer 2004
5. Copper wire #1 has a length L and a diameter d. Copper wire #2 has a length 2L and a diameter 2d. If R1 and R2
represent the resistance of wire #1 and wire #2, respectively, which statement is correct?
(A) R1  14 R2
(B) R1  12 R2
(C) R1  R2
(D) R1  2 R2
(E) R1  8R2
6. Kirchhoff's current (or junction) rule is a statement of the conservation of
(A)
(B)
(C)
(D)
(E)
energy.
momentum.
angular momentum.
charge.
electric flux.
7. In the circuit shown in the figure to the right, resistor R2 is variable,
and all other circuit elements are fixed. As the resistance of resistor
R2 is increased, the magnitude of the electric potential difference
across R2
E
(A)
(B)
(C)
(D)
R1
increases.
decreases.
remains constant.
may increase or decrease depending on whether R2  R3 is
greater than or less than R1 .
8. Consider the oscillator circuit demonstrated during lecture and
shown to the right. Recall that the tube lights with an orange
glow when the electric field inside the tube becomes large
enough to cause dielectric breakdown of the neon gas. As the
capacitor discharges through the tube, the potential difference
across the tube decreases and the neon light turns off. The
capacitor starts to charge again, and the process repeats. In
order to increase the flash rate (the number of flashes per
unit time), capacitance C must
(A) increase.
(B) decrease.
(C) This demonstration was never conducted.
3
R2
R3
neon gas
tube
C
PH2200 Practice Exam II
Summer 2004
9. A charged particle moves within a static magnetic field, that is, a magnetic field that does not change with time.
Assuming the magnetic force is the only force possibly acting on the charged particle, the particle
(A)
(B)
(C)
(D)
(E)
will always experience a magnetic force, regardless of its direction of motion.
may experience a magnetic force which will cause its speed to change.
may experience a magnetic force, but its speed will not change.
will always experience a magnetic force provided it starts from rest.
none of the above statements are true.
10. Shown below in Figure 10-1 is the side view of a cathode-ray tube. In the absence of a magnetic field and neglecting
the influence of gravity, electrons emitted from the electron gun at the rear of the tube travel along a horizontal line
and strike the screen at the center, forming a tiny dot. Now assume the cathode-ray tube is placed in a magnetic
field directed vertically upward as shown in Figure 10-2, the front view of the cathode ray tube. The electrons now
strike the screen and produce a dot at point
A
electron gun
D
electron beam
B
Figure 10-1
Side View of Cathode-Ray Tube
(A)
(B)
(C)
(D)
(E)
E
B
C
Figure 10-2
Front View of Cathode-Ray Tube
The Face of the Tube
A.
B.
C.
D.
E - the center of the screen, indicating there is no deflection of the electron beam.
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PH2200 Practice Exam II
Summer 2004
Problems: Each part of each problem is worth five points.
1. Consider an isolated conducting sphere having radius R1 and bearing charge Q .
(1-1) Assuming that the electric potential vanishes far from the sphere, the electric potential on the surface of the
sphere is
(A) 0
(B)
Q
4 o R12
Q
(C)
4 o R1
(D)
Q2
4 o R1
(E) none of the above.
The charged sphere described above is now connected by a very long straight wire to a second conducting sphere,
initially uncharged. The radius of the second sphere is R2 , and assume R1  R2 .
+Q - initial charge on sphere
R1
R2
(1-2) After equilibrium is reached, which of the following quantities is the same for both spheres?
(A)
(B)
(C)
(D)
(E)
electric charge
electric potential of the surface
magnitude of the electric field immediately above the surface
the flux of the electric field through a Gaussian sphere surrounding the conductor and concentric with it
none of the above
(1-3) What is the electric potential of the sphere having radius R1 after equilibrium is reached?
(A)
(B)
Q
4 o R1
Q  R1  R2 
4 o R1 R2
(C)
Q
4 o  R1  R2 
(D)
QR2
4 o R1  R1  R2 
(E)
Q
4 o  R1  R2 
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PH2200 Practice Exam II
Summer 2004
2. Consider the capacitor array shown in the figure to the right.
The array has been charged, and the source of emf has been
removed. The potential difference across the 4.00 μF
capacitor is known to be 10.0 V.
4.00 μF
(2-1) What is the equivalent capacitance of the array?
(A)
(B)
(C)
(D)
(E)
6.00 μF
1.00 μF
2.00 μF
3.00 μF
4.00 μF
6.00 μF
2.00 μF
  106
(2-2) What is the energy stored in the 4.00 μF capacitor?
(A)
(B)
(C)
(D)
(E)
100 μJ
200 μJ
300 μJ
400 μJ
500 μJ
(2-3) What is the charge on the 2.00 μF capacitor?
(A)
(B)
(C)
(D)
(E)
20.0 μC
40.0 μC
60.0 μC
80.0 μC
100 μC
(2-4) What is the potential difference across the 6.00 μF capacitor?
(A)
(B)
(C)
(D)
(E)
5.00 V
10.0 V
15.0 V
20.0 V
25.0 V
(2-5) If a dielectric is inserted between the plates of the 6.00 μF capacitor, the potential difference across the
4.00 μF capacitor will
(A) increase.
(B) decrease.
(C) remain at its original value of 10.0 V.
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PH2200 Practice Exam II
Summer 2004
3. Consider a string of Christmas tree lights containing eight (8) identical bulbs in parallel. The string is rated at
80.0 W and is connected across a 120 V source of emf.
(3-1) What is the equivalent resistance of the string?
(A)
(B)
(C)
(D)
(E)
100 
120 
140 
160 
180 
(3-2) What is the current through a single bulb?
(A)
(B)
(C)
(D)
(E)
0.0529 A
0.0646 A
0.0779 A
0.0833 A
0.0917 A
For the remaining parts of the problem, suppose one bulb in the string burns out, leaving a string with seven (7)
identical bulbs in parallel.
(3-3) What now is the current through a single bulb?
(A)
(B)
(C)
(D)
(E)
0.0529 A
0.0646 A
0.0779 A
0.0833 A
0.0917 A
(3-4) At what rate does the source of emf deliver energy to the string of remaining bulbs?
(A)
(B)
(C)
(D)
(E)
65.0 W
70.0 W
75.0 W
80.0 W
90.0 W
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PH2200 Practice Exam II
Summer 2004
4. The switch in the circuit shown to the right has been in position A
for a long time. It is changed to position B at time t  0 s. At this
time, the charge on the capacitor is 18.0 106 C .
A
B
(4-1) What is the emf E of the battery used to charge the capacitor?
(A)
(B)
(C)
(D)
(E)
50.0 
E
1.50 V
3.00 V
6.00 V
9.00 V
12.0 V
2.00  10
(4-2) What is the charge on the capacitor at t  50.0 106 s ?
(A)
(B)
(C)
(D)
(E)
7.37 106 C
9.01106 C
10.9 106 C
12.5 106 C
14.9 106 C
(4-3) What is the electric potential difference across the resistor at t  175 106 s ?
(A)
(B)
(C)
(D)
(E)
0.498 V
0.703 V
0.998 V
1.13 V
1.56 V
(4-4) What is the total energy dissipated by the resistor during the discharge of the capacitor?
(A)
(B)
(C)
(D)
(E)
81.0 106 J
112 106 J
247 106 J
296 106 J
335 106 J
8
6
F
PH2200 Practice Exam II
Summer 2004
5. A wire of length 0.250 m is supported by two identical columns of mercury as shown below. The height of each
column is 0.300 m and the resistance of each column is 7.35 102  . The entire structure is in a region of space
containing a uniform magnetic field of magnitude 0.0100 T directed into the plane of the page. When a 1.50 V
battery is connected between the pools of mercury, a current of 3.82 A passes through the wire, and the wire is in
equilibrium - barely maintaining contact with the mercury. The wire stays in contact with the mercury to maintain
the electrical connection, but the mercury exerts no force on the wire. Gravity acts downward in the figure below.
Assume g  9.80 m/s2 .



wire
0.250 m



7.35 102 
mercury
0.300 m
g
1.50 V Battery
(5-1) Does the current through the wire flow from (A) left to right (  ), or (B) right to left (  )?
(5-2) What is the mass of the wire?
(A) 8.37 104 kg
(B) 8.69 104 kg
(C) 8.93 104 kg
(D) 9.29 104 kg
(E) 9.74 104 kg
(5-3) Find the cross-sectional area of the columns of mercury. The resistivity of mercury is 98.0 108 Ω  m .
Assume the columns have a uniform cross-section - neglect the rounding at the top due to surface tension.
(A)
(B)
(C)
(D)
(E)
3.80  106 m2
4.00 106 m2
4.40 106 m2
4.80 106 m2
5.20  106 m2
(5-4) What is the resistance of the of the wire?
(A)
(B)
(C)
(D)
(E)
0.195 
0.246 
0.289 
0.317 
0.375 
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PH2200 Practice Exam II
Summer 2004
KEY
Name: ____________________________________
ID#
___________________________________________
Concept Questions
Problems
B
1. _______
C
1-1 _______
D
3-3 _______
A
2. _______
B
1-2 _______
B
3-4 _______
C
3. _______
C
1-3 _______
D
4-1 _______
E
4. _______
C
2-1 _______
C
4-2 _______
D
5. _______
B
2-2 _______
E
4-3 _______
D
6. _______
A
2-3 _______
A
4-4 _______
A
7. _______
B
2-4 _______
A
5-1 _______
B
8. _______
C
2-5 _______
E
5-2 _______
C
9. _______
E
3-1 _______
B
5-3 _______
B
10. _______
D
3-2 _______
B
5-4 _______
10
Subtotal 1 _______
10
Subtotal 2 _______
10
Subtotal 3 _______
30
Exam Score _______
10