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TIME
OF
COMPLETION_______________
NAME_____SOLUTIONS________________________
DEPARTMENT OF NATURAL SCIENCES
PHYS 2212, Exam 1
Version 1
Total Weight: 100 points
Section 1
March 17, 2014
1.
Check your examination for completeness prior to starting. There are a total of eleven
(11) problems on nine (9) pages.
2.
Authorized references include your calculator with calculator handbook, and the
Reference Data Pamphlet (provided by your instructor).
3.
You will have 75 minutes to complete the examination.
4.
The total weight of the examination is 150 points.
5.
There are six (6) multiple choice and five (5) calculation problems. Work five (5)
multiple choice and four (4) calculation problems. Show all work; partial credit will be given for
correct work shown.
6.
If you have any questions during the examination, see your instructor who will
be located in the classroom.
7.
Start:
Stop:
3:35 p.m.
4:50 p. m.
PROBLEM
POINTS
1-6
30
7
30
8
30
9
30
10
30
11
30
TOTAL
PERCENTAGE
CREDIT
1. Consider three resistors with unequal resistances connected in parallel to a battery. Which of
the following statements are true? Check all that apply.
a. The equivalent resistance of the combination of resistors is greater than the resistance of
any one of the three resistors.
b. The current flowing through each of the resistors is the same and is equal to the current
supplied by the battery.
c.
The equivalent resistance of the combination of resistors is less than the
resistance of any one of the three resistors.
d.
The algebraic sum of the currents flowing through each of the three resistors is
equal to the current supplied by the battery.
e.
The algebraic sum of the voltages across the three resistors is equal to the voltage
supplied by the battery.
f.
The voltage across each of the resistors is the same and is equal in magnitude to
the voltage of the battery.
2. Consider two copper wires with the same cross-sectional area. Wire A is twice as long as
wire B. How do the resistivities and resistances of the two wires compare? Check all that
apply.
a. Wire A has twice the resistance of wire B.
b.
Wire A and wire B have the same resistivity.
c.
Wire A has twice the resistivity of wire B.
d.
Wire B has twice the resistance of wire A.
e.
Wire A and wire B have the same resistance.
f. Wire B has twice the resistivity of wire A.
3. When a potential difference of 10 V is placed across a certain solid cylindrical resistor, the
current through it is 2 A. If the diameter of this resistor is now tripled, the current will be
a.
3 A.
b. 2/3 A.
c. 2/9 A.
d. 18 A.
e. 2 A.
4. Consider two capacitors with unequal capacitance connected in series to a battery. Which of
the following statements are true? Check all that apply.
a.
The sum of the charges stored on each capacitor is equal to the charge
supplied by the battery.
b. The voltage across each of the capacitors is the same.
c. The equivalent capacitance of the combination of the two capacitors is greater
than the capacitance of either of the capacitors.
d. The charge stored on each of the capacitors is the same.
e. The equivalent capacitance of the combination of the two capacitors is less than
the capacitance of either of the capacitors.
f. The algebraic sum of the voltages across the two capacitors is equal to the voltage
supplied by the battery.
5. Which of the following statements are true? Check all that apply.
a.
The potential energy of a test charge increases as it moves along an equipotential
surface.
b. The potential energy of a test charge decreases as it moves along an equipotential
surface.
c.
An equipotential surface is a three-dimensional surface on which the electric
potential is the same at every point.
d. Electric field lines and equipotential surfaces are always mutually perpendicular.
6. Five point charges q and four Gaussian surfaces S are represented in the figure shown.
Through which of the Gaussian surfaces are the total electric flux zero? Check all that
apply.
a.
S3
b. The total electric flux is not zero through any of the Gaussian surfaces.
c. S2
d. S1
e. S4
7. Four capacitors are connected across a 90-V voltage source as shown in the figure.
a. What is the charge on the 4.0-μF capacitor?
1 / C12  1 / C1  1 / C 2  3 / 4 F 1
C12 = 1.33F
Q2  Q12  C12 V12  120 C
b. What is the charge on a 2.0-μF capacitor?
Q1  Q12  C12 V12  120 C
c. What is the charge on the 3.0-μF capacitor?
1 / C34  1 / C3  1 / C 4  1 / 2 F 1
C34 = 2.00F
Q3  Q34  C34 V34  180 C
d. What is the potential difference across the 6.0-μF capacitor?
V4 
Q4 180 C

 30.0 V
C 4 6.00 F
e. What is the equivalent capacitance of the combination?
1 / C12  1 / C1  1 / C 2  3 / 4 F 1
C12 = 1.33F
1 / C34  1 / C3  1 / C 4  1 / 2 F 1
C34 = 2.00F
C1234=1.33 F + 2.00F = 3.33F
8.
A +4.0 μC-point charge and a -4.0-μC point charge are placed as shown in the figure.
a. What is the potential difference, VB – VA, between points A and B?
VA  ke
Q1
Q
 k e 2  4.794  10 4 V
r1
r2
VB  k e
Q1
Q
 k e 2  4.794  10 4 V
r1
r2
V  VB  V A  9.59  10 4 V
b. How much work is required to move a point charge of -2.0 C from point A to
point B?
W  qV  (2.00  10 6 C )(9.59  10 4 V )  0.192 J
9. Three identical point charges q= +2.00 C are placed at each of three corners of a square of
side 0.100 m.
a. Find the magnitude of the net force on a point charge - 3q placed at the center of
the square.
F1  F2  F3  k e
q(3q)
 21.58 N
l2
where l = 0.0707 m



o F
o
F
F
Directions of the forces: 1 at 135 , 2 at 45 , and 3 at -45o,


Adding three forces produces Ftot  (15.25 N )i  (15.25 N ) j with the magnitude of 21.58 N
b.
Find the direction of the net force on the point charge.
Direction: 45o
Easy check: because of the symmetry of the problem, the forces due to charge 1 and 3 cancel
each other so total force must correspond to the force due to charge 2.
10.For the circuit shown in the figure,
c. Find the equivalent resistance of the combination.
1
1
1
3



R12 R1 R2 16 
R12=16/3 
R123= R12 + R3=16/3  20  25.33 
1
1
1
4



R45 R5 R4 6 
R45=3/2 
1
R12345

1
1

 0.706 
R123 R45
R12345=1.416 
d. If the battery produces 120 V of potential difference what is the current in a 20.0
 resistor?
I3 
V123
 4.737 A
R123
e. What is the potential difference across the 6.0  resistor?
V  120 V
11. A portion of Nichrome wire of radius 3.90 mm is to be used in winding a heating coil. If the
coil must draw a current of 9.50 A when a voltage of 120 V is applied across its ends, find the
following. (Take the resistivity of nichrome to be1.50 10-6 Ω · m.)
a. The required resistance of the coil.
R
V
 12.63 
I
b. The length of wire you must use to wind the coil.
R
l
TIME
RA

l
A
 402 m
OF
COMPLETION_______________
NAME__SOLUTION___________________________
DEPARTMENT OF NATURAL SCIENCES
PHYS 2212, Exam 1
Version 2
Total Weight: 100 points
Section 1
March 17, 2014
1.
Check your examination for completeness prior to starting. There are a total of eleven
(11) problems on nine (9) pages.
2.Authorized references include your calculator with calculator handbook, and the Reference
Data Pamphlet (provided by your instructor).
3.
You will have 75 minutes to complete the examination.
4.
The total weight of the examination is 150 points.
5.
There are six (6) multiple choice and five (5) calculation problems. Work five (5)
multiple choice and four (4) calculation problems. Show all work; partial credit will be given for
correct work shown.
6.
If you have any questions during the examination, see your instructor who will
be located in the classroom.
7.
Start:
Stop:
3:35 p.m.
4:50 p. m.
PROBLEM
POINTS
1-6
30
7
30
8
30
9
30
10
30
11
30
TOTAL
PERCENTAGE
CREDIT
a. Consider three resistors with unequal resistances connected in series to a
battery. Which of the following statements are true? Check all that apply.
a. The equivalent resistance of the combination of resistors is greater than the resistance of
any one of the three resistors.
a. The current flowing through each of the resistors is the same.
b.
The equivalent resistance of the combination of resistors is less than the
resistance of any one of the three resistors.
c.
The algebraic sum of the currents flowing through each of the three resistors is
equal to the current supplied by the battery.
d.
The algebraic sum of the voltages across the three resistors is equal to the voltage
supplied by the battery.
e.
The voltage across each of the resistors is the same and is equal in magnitude to
the voltage of the battery.
b. Consider two copper wires with the same cross-sectional area. Wire A is twice
as long as wire B. How do the resistivities and resistances of the two wires
compare? Check all that apply.
a. Wire A has twice the resistance of wire B.
b.
Wire A and wire B have the same resistivity.
c.
Wire A has twice the resistivity of wire B.
d.
Wire B has twice the resistance of wire A.
e.
Wire A and wire B have the same resistance.
f. Wire B has twice the resistivity of wire A.
c. When a potential difference of 10 V is placed across a certain solid cylindrical
resistor, the current through it is 2 A. If the diameter of this resistor is now
tripled, the current will be
a.
3 A.
b. 2/3 A.
c. 2/9 A.
d. 18 A.
e. 2 A.
d. Consider two capacitors with unequal capacitance connected in parallel to a
battery. Which of the following statements are true? Check all that apply.
a.
The sum of the charges stored on each capacitor is equal to the
charge supplied by the battery.
b. The voltage across each of the capacitors is the same.
c. The equivalent capacitance of the combination of the two capacitors is
greater than the capacitance of either of the capacitors.
d. The charge stored on each of the capacitors is the same.
e. The equivalent capacitance of the combination of the two capacitors is
less than the capacitance of either of the capacitors.
f. The algebraic sum of the voltages across the two capacitors is equal to
the voltage supplied by the battery.
e. Which of the following statements are true? Check all that apply.
a.
The potential energy of a test charge increases as it moves along an
equipotential surface.
b. The potential energy of a test charge decreases as it moves along an
equipotential surface.
c.
PHYS 2212 Exam 1, Version 1
Spring 2014
An equipotential surface is a three-dimensional surface on which the
electric potential is the same at every point.
14
d. Electric field lines and equipotential surfaces are always mutually
perpendicular.
f. Five point charges q and four Gaussian surfaces S are represented in the figure
shown. Through which of the Gaussian surfaces are the total electric flux
zero? Check all that apply.
a.
S3
b. The total electric flux is not zero through any of the Gaussian surfaces.
c. S2
d. S1
e. S4
g. Four capacitors are connected across a 90-V voltage source as shown in the
figure.
PHYS 2212 Exam 1, Version 1
Spring 2014
15
1. What is the charge on the 6.0-μF capacitor?
1 / C34  1 / C3  1 / C 4  1 / 2 F 1
C34 = 2.00F
Q4  Q34  C34 V34  180 C
2. What is the charge on a 2.0-μF capacitor?
Q3  Q34  C34 V34  180 C
3. What is the charge on the 3.0-μF capacitor?
1 / C12  1 / C1  1 / C 2  3 / 4 F 1
C12 = 1.33F
Q1  Q12  C12 V12  120 C
4. What is the potential difference across the 6.0-μF capacitor?
PHYS 2212 Exam 1, Version 1
Spring 2014
16
V2 
Q2 120 C

 30.0 V
C 2 4.00 F
5. What is the equivalent capacitance of the combination?
1 / C12  1 / C1  1 / C 2  3 / 4 F 1
C12 = 1.33F
1 / C34  1 / C3  1 / C 4  1 / 2 F 1
C34 = 2.00F
C1234=1.33 F + 2.00F = 3.33F
h.
A +4.0 μC-point charge and a -4.0-μC point charge are placed as shown in the
figure.
a. What is the potential difference, VB – VA, between points A and B?
VA  ke
Q1
Q
 k e 2  4.794  10 4 V
r1
r2
PHYS 2212 Exam 1, Version 1
Spring 2014
17
VB  k e
Q1
Q
 k e 2  4.794  10 4 V
r1
r2
V  VB  V A  9.59  10 4 V
b. How much work is required to move a point charge of +3.0 C from
point A to point B?
W  qV  (3.00  10 6 C )(9.59  10 4 V )  0.288 J
9. Three identical point charges q= +2.00 C are placed at each of three corners of a square of
side 0.100 m.
a. Find the magnitude of the net force on a point charge - 3q placed at the empty
corner of the square.
F1  F3  k e
F2  k e
q(3q)
 10.79 N
l2
where l = 0.100 m
q(3q)
 5.43 N
l2
where l = 0.141 m



o F
o
F
F
1
2
Directions of the forces: at 90 ,
at 45 , and 3 at 0o,
PHYS 2212 Exam 1, Version 1
Spring 2014
18


F

(
14
.
62
N
)
i

(
14
.
62
N
)
j with the magnitude of 20.68 N
tot
Adding three forces produces
b.
Find the direction of the net force on the point charge.
Direction: 45o
10.For the circuit shown in the figure,
c. Find the equivalent resistance of the combination.
1
1
1
3



R12 R1 R2 16 
R12=16/3 
R123= R12 + R3=16/3  20  25.33 
1
1
1
4



R45 R5 R4 6 
R45=3/2 
1
R12345

1
1

 0.706 
R123 R45
R12345=1.416 
PHYS 2212 Exam 1, Version 1
Spring 2014
19
d. If the battery produces 100 V of potential difference what is the
current in a 20.0  resistor?
I3 
V123
 3.95 A
R123
e. What is the potential difference across the 2.0  resistor?
100 V
11. A portion of Nichrome wire of radius 2.90 mm is to be used in winding a heating coil. If the
coil must draw a current of 8.50 A when a voltage of 120 V is applied across its ends, find the
following. (Take the resistivity of nichrome to be1.50 10-6 Ω · m.)
5.
R
The required resistance of the coil.
V
 14.11 
I
6.
The length of wire you must use to wind the coil.
R
l
RA

l
A
 249 m
PHYS 2212 Exam 1, Version 1
Spring 2014
20