Mark answers in spaces 76-105 on the answer sheet
PHYSICS 221
Spring 2004
Final Exam: May 5 2004 12:00pm—2:00pm
Name (printed): ____________________________________________
ID Number: ______________________________________________
Section Number: __________________________________________
INSTRUCTIONS:
Each question is of equal weight, answer all questions. All questions are multiple choice.
Before turning over this page, put away all materials except for pens, pencils, erasers,
rulers, your calculator and “aid sheet”. An “aid sheet” is one two sided 8½×11 page of
notes prepared by the student. Note also formula sheets pages 15-20.
"In general, any calculator, including calculators that perform graphing numerical
analysis functions, is permitted. Electronic devices that can store large amounts of text,
data or equations are NOT permitted." If you are unsure whether or not your calculator
is allowed for the exam ask your TA.
Examples of allowed calculators: Texas Instruments TI-30XII/83/83+/89, 92+
Casio FX115/250HCS/260/7400G/FX7400GPlus/FX9750 Sharp EL9900C.
Examples of electronic devices that are not permitted: Any laptop, palmtop, pocket
computer, PDA or e-book reader.
In marking the multiple choice bubble sheet use a number 2 pencil. Do NOT use ink. If
you did not bring a pencil, ask for one. Fill in your last name, middle initial, and first
name. Your ID is the middle 9 digits on your ISU card. Special codes K to L are your
recitation section , for the Honors section please encode your section number as follows:
H1⇒02; H2⇒13 and H3⇒31. If you need to change any entry, you must completely
erase your previous entry. Also, circle your answers on this exam. Before handing in your
exam, be sure that your answers on your bubble sheet are what you intend them to be.
It is strongly suggested that you circle your choices on the question sheet. You
may also copy down your answers on the record sheet and take this page with you for
comparison with the answer key to be posted later.
When you are finished with the exam, place all exam materials, including the bubble
sheet, and the exam itself, in your folder and return the folder to your recitation
instructor. No cell phone calls allowed. Either turn off your cell phone or leave it at home.
Anyone answering a cell phone must hand in their work; their exam is over. There are 30
questions on this exam labeled 76-105 organized into 3 parts: Part A contains questions
76-95; Part B consists of questions 96-100; Part C consists of questions 101-105.
Mark answers in spaces 76-105 on the answer sheet.
Best of luck, David Atwood and Anatoli Frishman
Physics 221 2004 S Final Exam
Page 1 of 23
Mark answers in spaces 76-105 on the answer sheet
Part A: Questions 76-95 (20 questions):
[Based on Lectures 1-41]
G
G
[76] Vectors A and B start at a corner of a cube of edge
G
length 1. Vector A lies along the edge of the cube. Vector
G
B goes to the opposite corner of the cube. What is the
G G
value of A ⋅ B ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 2
1
[77] A rock is thrown upwards from a bridge 20.0m above level ground. The initial
upwards velocity of the rock is 10.0m/s. How fast is the rock moving when it hits the
ground? Neglect air resistance:
(A) 17.2 m/s
(B) 19.8 m/s
(C) 22.2 m/s
(D) 25.0 m/s
(E) 27.2 m/s
[78] The Figure at right shows the
trajectories of three cannon balls fired
simultaneously. In which order do they
strike the ground? Neglect air resistance.
(A) P Q R
(B) R Q P
(C) R P Q
(D) Q P R
(E) Cannot be determined without
more information.
Physics 221 2004 S Final Exam
Page 2 of 23
[79] Four blocks of mass mP=4kg, mQ=3kg, mR=2kg, mS=1kg are on a frictionless
horizontal surface as shown on the figure below. The blocks are connected by ideal
massless strings. A force FL=30N is applied to the left block and is directed to the left.
Another force FR=50N is applied to the right block, and is directed to the right. What is
the magnitude of the tension T in the string between mQ and mR.
T=?
FL=30N
mP=4kg
mQ=3kg
mR=2kg
mS=1kg
FR=50N
(A) T=14N
(B) T=20N
(C) T=30N
(D) T=36N
(E) T=44N
[80] The body that is suspended by a massless rope has weight of 75N. The rope is
pulling the body up at decreasing speed. Is the tension in the rope is
(A) 75 N
(B) greater than 75 N
(C) less than 75 N
(D) there is not enough information to distinguish between the answers A, B and C
(E) 0 N
[81] A block of mass 10kg lies at rest on a floor. The coefficients of static friction
between the block and the floor is µS=0.4. The coefficient of kinetic friction between the
block and the floor is µK=0.3. What is the magnitude of the frictional force on the block?
(A) 40N
(B) 30N
(C) 4N
(D) 3N
(E) 0
Physics 221 2004 S Final Exam
Page 3 of 23
[82] A simple pendulum has a string of length L=2m and a bob of mass 4kg. The bob
is pulled back through an angle of 30º and released from rest. What is
•
the kinetic energy of the bob when the string is vertical?
(A) 78.4J
2m
(B) 39.2J
30º
(C) 67.7J
(D) 10.5J
(E) 21.0J
4 kg
K=?
[83]
Particles Q, R, S, T have the masses and momenta given in the following table:
Particle
Q
R
S
T
Mass
m0
2m0
m0
2m0
Momentum
p0
p0
2p0
2p0
Particle Q has mass m and momentum p0. Particle
R has mass 2m0 and momentum p0. Particle S has
mass m and momentum 2p0. Particle T has mass
2m0 and momentum 2p0.
If the kinetic energy of these particles is KQ, KR, KS and KT respectively. Which of the
following statements concerning the relative size of the kinetic energy is true?
(A) KP<KQ<KR<KS
(B) KP<KR<KQ<KS
(C) KQ<KP<KS<KR
(D) KP=KQ=KS<KR
(E) KR<KQ<KT<KS
Physics 221 2004 S Final Exam
Page 4 of 23
[84] The first diagram below shows xcomponent ( Fx ) of a conservative force as
a function of position for a particle
confined to move along the x-axis. Which
of the following diagrams correctly
indicates the corresponding graph of
potential energy U as a function of
position.
(A) Graph A
(B) Graph B
(C) Graph C
(D) Graph D
(E) Graph E
Physics 221 2004 S Final Exam
Page 5 of 23
2m
[85] Consider a square slab of uniform
density and mass 10kg is resting on its
edge. How much work does it take to
rotate the slab 45º so that it is balanced on
its corner?
(A) 98 J
(B) 138 J
(C) 41 J
(D) 82 J
(E) 196 J
2m
[86] Consider a system that consists of four 2kg masses
connected by massless rods and arranged in a square with edge
length 4m. What is the moment of inertial of the system about the
axis going through the diagonal of the square?
(A) 4 kg m²
(B) 8 kg m²
(C) 16 kg m²
(D) 32 kg m²
(E) 64 kg m²
2kg
4m
4m
2kg
4m
4m
[87] A skater is spinning on a vertical axis with her arms extended. She pulls in her
arms and her angular velocity increases. Which of the following statements most
accurately describes the situation:
(A) The rotational kinetic energy of the skater remains the same as she pulls in her
arms.
(B) The angular momentum of the skater remains the same as she pulls in her arms.
(C) The period of the skater’s rotation remains the same as she pulls in her arms.
(D) Both the rotational kinetic energy and angular momentum of the skater remains
the same as she pulls in her arms.
(E) The rotational kinetic energy of the skater decreases as she pulls in her arms.
Physics 221 2004 S Final Exam
Page 6 of 23
2kg
2kg
[88] A 1.00m long rod of uniform mass distribution
weighing 200N is supported at its ends by wires A and B.
A 100N weight is attached to the rod 10cm from wire A.
What is the tension in wire A if the system is in
equilibrium?
(A) 95N
(B) 100N
(C) 109N
(D) 190N
(E) 200N
[89] Consider an asteroid which orbits the
sun in the elliptical orbit shown. The closest
approach to the sun at point A is 2AU while
the farthest the asteroid moves from the sun
is 8AU at point B. What is the ratio between
the velocity of the asteroid at point A, vA
and the velocity of the asteroid at point B,
vB? (1AU= average distance between the
Sun and the Earth)
(A) v A : v B = 1 : 1
(B) v A : v B = 2 : 1
(C) v A : v B = 4 : 1
(D) v A : v B = 8 : 1
(E) v A : v B = 16 : 1
1.00m
200N
100N
Sun
•
2AU
•
8AU
[90] What is the angular frequency of small oscillation of a square picture with side
length 1m which is hung by the corner. Assume that the square has uniform density.
(A) ω=3.22 s-1
(B) ω=4.56 s-1
(C) ω=6.45 s-1
(D) ω=2.90 s-1
(E) ω=5.80 s-1
Physics 221 2004 S Final Exam
Suspension Point
1m
1m
Page 7 of 23
[91] A, B and C are three uniformly charged rods with their axes parallel to the y-axis.
These rods are equally spaced as shown below where the spacing is small compared to
the length of the rods. The charge on rod A is Q, the
charge on rod B is 2Q and the charge on rod C is 3Q.
y
What is the ratio between the x component of the
electrostatic force on rod A, FAx to the electrostatic force
on rod B, FBx.
(A) FAx:FBx= +7:8
(B) FAx:FBx= +11:16
(C) FAx:FBx= +1:1
(D) FAx:FBx= −11:16
(E) FAx:FBx= −7:8
x
Q
2Q 3Q
[92] Consider three particles of charge Q arranged in an equilateral
triangle. How much net work does it take to move one of the particles
to a point exactly half way in between the other two while keeping
those two charges fixed?
(A) 0
(B) kQ²/L
(C) (3/2) kQ²/L
(D) 2kQ²/L
(E) 4kQ²/L
+Q
L
L
+Q
W=?
L
[93] A capacitor consists of two circular disks of radius 10cm which are separated by a
distance of 1mm. What is the capacitance?
(A) 28 pF
(B) 140 pF
(C) 28 nF
(D) 70 pF
(E) 278 pF
Physics 221 2004 S Final Exam
Page 8 of 23
+Q
[94] A parallel plate capacitor consists of two plates separated by a distance d. It is
attached to a battery and an amount of energy U is stored in the capacitor. While it is
connected to the battery, the distance between the two plates is increased to 2d. What is
the energy stored in the capacitor after the distance is increased?
(A) U/4
(B) U/2
(C) U
(D) 2U
(E) 4U
[95] How much current will be supplied by the
battery in the circuit shown?
(A)
(B)
(C)
(D)
(E)
1A
2A
3A
4A
6A
4Ω
12V
3Ω
I=?
Physics 221 2004 S Final Exam
Page 9 of 23
6Ω
Part B: Questions 96-100 (5 questions) [Based on Lectures 33-41]
[96]
A parallel plate capacitor consists of two plates separated by a distance d. It is
attached to a battery and an amount of energy U is stored in the capacitor. It his then
disconnected from the battery and the plates are insulated so the charge on the plates
remains constant. The distance between the two plates is then increased to 2d. What is the
energy stored in the capacitor after the distance is increased?
(A) U/4
(B) U/2
(C) U
(D) 2U
(E) 4U
[97] Consider the two capacitors depicted. Both
are parallel plate capacitors with the same area of
plates and the same separation between the plates.
Capacitor #1 has vacuum between the plates and the
capacitance of this capacitor is C1. Capacitor #2 has
the lower half of the space filled with a dielectric of
dielectric constant κA and the upper half of the
space is filled with a dielectric of dielectric constant
κB. Assuming the spacing of the gap is much
smaller than the dimensions of the plate, which of
the following is the best estimate of the capacitance
of #2, C2?
2
C1
(A) C 2 =
1/ κ A + 1/ κ B
1
C1
(B) C 2 =
1/ κ A + 1/ κ B
(C) C 2 = (κ A + κ B )C1
(D) C 2 = 12 (κ A + κ B )C1
C1
Capacitor #1
Vacuum
κA
Capacitor #2
κB
(E) C 2 = κ Aκ B C1
Physics 221 2004 S Final Exam
C2
Page 10 of 23
[98] What is the magnitude of the current through the 4Ω
resistor in the circuit diagram shown?
(A) 0.25 A
(B) 0.50 A
(C) 1.00 A
(D) 2.00 A
(E) 4.00 A
[99] In the circuit diagram shown at right what is the
charge on the 1F capacitor?
(A) 4C
(B) 8C
(C) 12C
(D) 15C
(E) 36C
[100] An infinitely long uniformly charged wire has charge density of λ=+1 µC/m.
How much work must be preformed by an external force on a +2 µC charge to move it
from a point 10cm from the wire to a point 1cm from the wire?
(A) +0.083J
(B) +0.041J
(C) -0.021J
(D) –0.083J
(E) –0.041J
Physics 221 2004 S Final Exam
Page 11 of 23
Part C: Questions 101-105 (5 questions) [Lab Questions]
[101]
Consider a cart whose position is measured with an
ultrasonic transducer (a “motion detector”), as you did in lab.
(Assume the sensor gives positions relative to the X axis illustrated in
the figure).
Which of the following represents a graph of position vs. time that
might result when the cart is accelerating at a fixed, positive rate?
A
X
X
B
X
t
t
E)
C
X
X
0
D
t
t
None of the above graphs.
L
two cells, chain,
seat and subject
R
W
Y
X
W
X component
0
L
-56.2
R
+57.1
[102] In the "Forces and Vectors" lab, you accumulated data similar to that shown
above (for simplicity, we consider only the X components). Assume that, done with care,
the procedure and apparatus which you used yields results (for each of the components of
L, R, and W) that have an uncertainty (for each) that may be as large as ± 1%.
With this in mind, are the experimental results shown in the table above consistent with
theoretical expectations? Which of the following is the most suitable response?
(A) The data are not consistent with theoretical expectations, and the uncertainties typical of
this apparatus have little to do with this conclusion.
(B) The data are not consistent with theoretical expectations, given the uncertainties expected
for this apparatus.
(C) The data are consistent with theoretical expectations, given the uncertainties expected for
this apparatus
(D) The data are not consistent with the theoretical predictions; this indicates that the
particular apparatus used needs repair.
(E) One cannot say anything based upon the information given.
Physics 221 2004 S Final Exam
Page 12 of 23
[103] Using the rotating wheel apparatus such as you used in lab, a disk (which is not
spinning) is dropped concentrically upon the wheel as it is rotating freely. Assume that the
disk has a moment of inertia of 0.5 I0 , where I0 is the moment of inertia of the rotating
wheel. Which of the following graphs best represents the angular velocity, ω, as a function
of time before, during, and after the disk is dropped?
ω
A
ω
t
B
ω
t
C
ω
D
t
ω
E
t
[104] Consider two air pucks (made of some unknown
material) which can slide upon a smooth horizontal surface
with little friction, leaving trails of spark marks, with marks
produced at a fixed frequency. The pucks are of equal mass,
and are pushed (and released) toward one another, and then
collide. Assume that the pucks rotate little before and after the
collision.
For the record shown above, select the comment listed below which is most appropriate.
(A) The data looks O.K., although the collision clearly is not elastic.
(B) The data must be invalid since clearly momentum is not conserved.
(C) The data must be invalid since the collision clearly is not elastic.
(D) The data looks O.K.; both momentum and mechanical energy appear to be
conserved.
(E) One must know the time between sparks to make a definitive statement.
NOTE: By the data being invalid is meant that, for the situation described, such
data is impossible. To obtain such data, then some large extraneous factor must be
at work (such as hidden magnets, angels, etc.)
Physics 221 2004 S Final Exam
Page 13 of 23
t
[105] Consider a hollow metal sphere mounted on a thin insulating rod. Using
standard apparatus (e.g., an electrophorus), the largest possible electric charge is
placed on the sphere.
Where is the electric field largest, and for a sphere of a given size, what factor
determines the magnitude of the maximum charge?
location where electric
field is largest
A
B
C
D
E
surface of sphere
surface of sphere
center of sphere
center of sphere
none of the above
Physics 221 2004 S Final Exam
factor that determines the
magnitude of the maximum charge
dielectric strength of air
type of metal
dielectric strength of air
type of metal
Page 14 of 23
Formula Sheet for Exam 1
1. Physical Constants
(numerical value used to derive answers in exam):
1.1) Acceleration of gravity on Earth’s Surface: g=9.8m/s²
1.2) Radius of Earth: Rearth=6.38×106m
1.3) Mass of Proton: mp=1.67×10-27kg
3. Vectors
G G
G G
3.1) Dot Product: A ⋅ B = Ax B x + Ay B y + Az B z =| A || B | cosθ
G
G
where θ is the angle between A and B .
G
3.2) Components: A = Ax iˆ + Ay ˆj + Az kˆ
G
G G
3.3) Magnitude: | V |= V = V x2 + V y2 + V z2 = V ⋅ V
5. One Dimensional Motion
5.1) Average Velocity: v = ∆x / ∆t
5.2) Instantaneous Velocity: v = dx / dt
2. Calculus
2.1)
d
dx
x n = nx n −1
d
dx
sin x = cos x
x n +1
n +1
d
dx cos x = − sin x
n
∫ x dx =
4. Algebra
4.1) The solutions to ax 2 + bx + c = 0
are x =
1
2a
(− b ±
b 2 − 4ac
)
6. Forces
G
G
6.1) Newton’s Second: F = ma
G
G
6.2) Newton’s Third: FAB = − FBA
6.2) Kinetic Friction: f k = µ k N
6.4) Static Friction: f s ≤ µ s N
6.5) Centripetal Force: F =
v x = v0 x + a x t
x = x0 + v0 x t + 12 a x t 2
5.3) For Constant Acceleration only: v 2 − v 2 = 2a ( x − x )
0x
0
x
x
x − x0 1
= 2 (v x + v 0 x )
t
7. Three Dimensional Motion
G
7.1) Position Vector: r = xiˆ + yˆj + zkˆ
G
G
G
G
2 G
7.2) Velocity and Acceleration: v = dtd r
a = dtd v = dtd 2 r
G G G
v = v0 + at
G G G
G
r = r0 + v 0 t + 12 at 2
7.3) Constant Acceleration only: v 2 − v 2 = 2aG ⋅ (rG − rG )
0
G G0
r − r0 1 G G
= 2 (v + v 0 )
t
ω = 2πf
v = Rω
7.4) Circular Motion: f = 1 / T
7.4a) Angular Velocity: ω = dθ / dt
7.5) Centripetal Acceleration: a rad = Rω 2 = v 2 / R = ( 4π 2 R ) / T 2
G
G
G
7.6) Changing Reference Frames: v PA = v PB + v BA
Physics 221 2004 S Final Exam
Page 15 of 23
mv 2
R
Formula Sheet for Exam 2
8. Kinetic Energy and Work
8.1) Linear Motion: K = 12 mv 2
8.2) Rotational Motion: K rot = 12 Iω 2
G G
8.3) Work by a constant force W = F ⋅ s = Fs cosθ
8.4) Work done by a variable force in 1 dim:
9. Potential Energy
9.1) Gravitational: Ugrav=mgy
9.2) Spring: Uspring=kx²/2
9.3) Force from potential in 1D: Fx ( x) = −
dU
dx
x2
W = ∫ Fx dx
x1
G G P2
8.5) Work in 3D: W = ∫ F ⋅ dl = ∫ F cos φ dl
P2
P1
8.6) Power: P=dW/dt
P1
G G
P = F ⋅v
10. Momentum and Impulse
G
G
G G
10.1) Momentum: p = mv F = ddtp
G t2 G
G
G
10.2) Impulse: J = ∫ Fnet dt = p 2 − p1
t1
G
G
10.3) Center of mass position: M tot rcm = ∑ mi ri
G
G
10.4) Center of mass velocity: M tot vcm = ∑ pi
G
G
G
10.5) Center of mass acceleration: M tot a cm = ∑ Fi = Fexternal
11. Collisions
11.1) 1-dimensional totally inelastic collision: v1 f = v 2 f = v cm
11.2) 1-dimensional elastic collision:
v1 f = 2vcm − v1i
v 2 f = 2vcm − v 2i
G
G
G
11.3) 3-dimensional totally inelastic collision: v1 f = v 2 f = v cm
Physics 221 2004 S Final Exam
12. Rotation
12.1) Angular velocity ω = ddtθ
12.2) Angular Acceleration α =
dω
dt
2
12.3) Circular motion: a rad = Rω ; a tan = rα .
12.4) Moment of Inertia: I = ∑ mi Ri2
12.5) Parallel Axis Thm.: I P = I cm + Md 2
G G G
12.6) Torque: τ = r × F
Page 16 of 23
Physics 221 2004 S Final Exam
Page 17 of 23
Formula Sheet for Exam 3
13. Physical Constants
13.1) Gravitational Constant G=6.673×10−11 Nm²/kg²
13.2) Coulomb’s Constant k E = 4πε1 0 = 8.9876 × 109 Nm 2 / C 2
13.3) Permeability of vacuum ε 0 = 8.8542 × 10−12 C 2 /( Nm 2 )
13.4) Magnitude of electron charge e=1.6022x10-19 C
13.5) Mass of electron me = 9.11 × 10 −31 kg
14. Angular Momentum
G G G
14.1) For Particle L = r × p
G
G
14.2) For rigid body L = Iω
G
G dL
14.3) Relation to torque τ =
dt
18. Coulombs Law etc.
18.1) Coulomb’s Law: F = k E q1q2 / r 2
G
18.2) Electric Field from charge E = k E Qrˆ / r 2
G
G
18.3) Force exerted by an electric field: F = qE
15. Static Equilibrium
G
G
15.1) Condition for static equilibrium: τ net = 0; Fnet = 0
16. Gravity
16.1) Newton’s Law of Gravitational Attraction: F = G
m1m2
r2
m1m2
r
M
16.3) Acceleration of gravity g = G 2
r
16.4) Escape velocity ve = 2 gR = GM / R
19. Gauss’s Law
19.0) General definition of electric flux :
G G
Φ E = ∫ E cos φ dA = ∫ E⊥ dA = ∫ E ⋅ dA
19.1) Gauss’s Law Φ E = qenclosed / ε 0
19.2) Inside a conductor: E=0; ρ=0
19.3) Electric Field near a charged sheet:
E = σ /(2ε 0 )
16.2) Gravitational Potential U = −G
17. Harmonic Oscillation
17.1) Period/frequency: f = 1 / T
ω = 2π f = 2π / T
17.2) Force law for harmonic motion: F = −kx
17.3) Angular frequency of oscillator: ω = k / m
17.4) Solution to oscillator x = A cos(ωt + φ )
17.5) Simple pendulum ω =
g/L
17.6) Physical Pendulum ω = mgd / I
Physics 221 2004 S Final Exam
20. Kepler’s Laws
20.1) Each planet moves in an elliptical orbit
with the sun at one focus of the ellipse.
20.2) A line from the sun to a given planet
sweeps out equal areas in equal times.
Equivalently, the angular momentum of a
planet about the sun remains constant.
20.3) The periods of the planets are
proportional to the 3/2 power of the semimanor axis lengths of the orbit. If a is the
2πa 3 / 2
.
length of the semi-major axis, T =
Gmsun
Page 18 of 23
Additional Formula Sheet for Final Exam
21. Various Fields and Potentials
Case
Electric Field
Magnitude
Point Charge Q
E=
Q
4πε 0 r
Line charge, charge
per unit length λ
E=
λ
2πε 0 r
Charged sheet, charge
per unit area σ
E=
σ
2ε 0
Q
4πε 0 r
λ
ln[r / R ]
2πε 0
(R=arbitrary constant)
σ
V =
r
2ε 0
V =−
23. Potential and E-Field
G G
23.1) Potential from E-Field: Vb − Va = − ∫ E ⋅ dl
q1 q 2
r12
b
a
22.2) Energy density of an Electric Field: u = 12 ε 0 E 2
∂V
∂x
∂V
23.2) E-Field from Potential: E y = −
∂y
∂V
Ez = −
∂z
Ex = −
24. Capacitors
24.1) Basic Property: C =
V =
2
22. Electric Potential Energy
22.1) A pair of charges: U = k E
Potential
Q
V
A
d
1
1
1
1
1
=
+
+
+" +
Ceq C1 C2 C3
Cn
24.2) Parallel Plate Capacitor: C = ε 0
24.3) Capacitors in Series:
24.4) Capacitors in Parallel: Ceq = C1 + C2 + C3 + " + Cn
Q2
24.5) Energy Stored in a capacitor: U = QV = CV =
2C
A
24.2) Parallel Plate Capacitor with dielectric: C = κε 0
d
1
2
1
2
2
Physics 221 2004 S Final Exam
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Additional Formula Sheet for Final Exam (cont.)
25. Resistors
25.1) Basic Property (Ohm’s Law): V = IR
L
25.2) Resistance of a wire R = ρ
A
1
1
1
1
1
=
+
+
+" +
25.3) Resistors in Parallel:
Req R1 R2 R3
Rn
25.4) Resistors in Series: Req = R1 + R2 + R3 + " + Rn
25.5) Power Dissipated by Resistor: P = IV = RI 2 =
V2
R
26. Resistivity
G
G
26.1) Microscopic Ohm’s Law: E = ρJ
26.2) Conductivity: ρ = 1 / σ
26.3) Current from current density in a
wire: I = JA
27. Kirchhoff’s Rules
27.1) The sum of all currents flowing into a
junction is 0
27.2) The sum of potential differences
around a loop is 0.
28. RC Circuits
28.1) Time constant τ = RC
28.2) Charge on a capacitor discharging
through a resistor: Q = Q0e
−
t
τ
Physics 221 2004 S Final Exam
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Record Sheet
You may fill in this sheet with your choices, detach it and take it with you after the exam
for comparison with the posted answers
51
81
91
101
52
82
92
102
83
93
103
74
84
94
104
75
85
95
105
76
86
96
77
87
97
78
88
98
79
89
99
80
90
100
Physics 221 2004 S Final Exam
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Scratch Paper (intentionally left blank)
Physics 221 2004 S Final Exam
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Scratch Paper (intentionally left blank)
Physics 221 2004 S Final Exam
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