Electricity and Magnetism Full-Length Practice Paper 2 Questions | AP Physics C Electricity and Magnetism - Grade 9 PDF Download

 Page 1


AP Physics C: Electricity and Magnetism Practice Test 2
Page 2


AP Physics C: Electricity and Magnetism Practice Test 2
GO ON TO THE NEXT PAGE.
Section I
  
CONSTANTS AND CONVERSION FACTORS
Proton mass,
Neutron mass,
Electron mass,
Avogadro’s number,
Universal gas constant,
Boltzmann’s constant,
m
p
 = 1.67 × 10
–27
 kg
m
n
 = 1.67 × 10
–27
 kg
m
e
 = 9.11 × 10
–31
 kg
N
A
 = 6.02 × 10
23
 mol
–1
R = 8.31 J/(mol K)
k
B
 = 1.38 × 10
–23
 J/K
Electron charge magnitude,
1 electron volt,
Speed of light,
Universal gravitational constant,
Acceleration due to gravity 
at Earth’s surface,
e  = 1.60 × 10
–19
 C
1 eV = 1.60 × 10
–19
 J
c = 3.00 × 10
8
 m/s
G = 6.67 × 10
–11
 (N•m
2
)/kg
2
g = 9.8 m/s
2
1 unified atomic mass unit,
Planck’s constant,
Vacuum permittivity,
Coulomb’s law constant,
Vacuum permeability,
Magnetic constant,
1 atmosphere pressure,
1 u = 1.66 × 10
–27
 kg = 931 MeV/c
2
h = 6.63 × 10
–34
 J•s = 4.14 × 10
–15
 eV•s
hc = 1.99 × 10
–25
 J•m = 1.24 × 10
3
 eV•nm
e
0
 = 8.85 × 10
–12
 C
2
/(N•m
2
)
k = 1/(4pe
0
) = 9.0 × 10
9
 (N•m
2
)/C
2
µ
0
 = 4p × 10
–7
 (T•m)/A
k' = µ
0
/(4p) = 1 × 10
–7
 (T•m)/A
1 atm = 1.0 × 10
5
 N/m
2
 = 1.0 × 10
5
 Pa
UNIT 
SYMBOLS
meter, m mole, mol watt, W farad, F
kilogram, kg hertz, Hz coulomb, C tesla, T
second, s newton, N volt, V degree Celsius, °C
ampere, A pascal, Pa ohm, ? electron volt, eV
kelvin, K joule, J henry, H
V ALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
? 0° 30° 37° 45° 53° 60° 90°
sin? 0 1/2 3/5 22 / 4/5 32 / 1
cos? 1 32 / 4/5 22 / 3/5 1/2 0
tan? 0 33 / 3/4 1 4/3 3 ¥
PREFIXES
Factor Prefix Symbol
10
9
giga G
10
6
mega M
10
3
kilo k
10
–2
centi c
10
–3
milli m
10
–6
micro µ
10
–9
nano n
10
–12
pico p
   
ADV ANCED PLACEMENT PHYSICS C TABLE OF INFORMATION
The following assumptions are used in this exam.
 I. The frame of reference of any problem is inertial unless otherwise 
stated.
 II. The direction of current is the direction in which positive charges 
would drift.
 III. The electric potential is zero at an infinite distance from an isolated 
point charge.
 IV . All batteries and meters are ideal unless otherwise stated.
 V . Edge effects for the electric field of a parallel plate capacitor are 
negligible unless otherwise stated.
Page 3


AP Physics C: Electricity and Magnetism Practice Test 2
GO ON TO THE NEXT PAGE.
Section I
  
CONSTANTS AND CONVERSION FACTORS
Proton mass,
Neutron mass,
Electron mass,
Avogadro’s number,
Universal gas constant,
Boltzmann’s constant,
m
p
 = 1.67 × 10
–27
 kg
m
n
 = 1.67 × 10
–27
 kg
m
e
 = 9.11 × 10
–31
 kg
N
A
 = 6.02 × 10
23
 mol
–1
R = 8.31 J/(mol K)
k
B
 = 1.38 × 10
–23
 J/K
Electron charge magnitude,
1 electron volt,
Speed of light,
Universal gravitational constant,
Acceleration due to gravity 
at Earth’s surface,
e  = 1.60 × 10
–19
 C
1 eV = 1.60 × 10
–19
 J
c = 3.00 × 10
8
 m/s
G = 6.67 × 10
–11
 (N•m
2
)/kg
2
g = 9.8 m/s
2
1 unified atomic mass unit,
Planck’s constant,
Vacuum permittivity,
Coulomb’s law constant,
Vacuum permeability,
Magnetic constant,
1 atmosphere pressure,
1 u = 1.66 × 10
–27
 kg = 931 MeV/c
2
h = 6.63 × 10
–34
 J•s = 4.14 × 10
–15
 eV•s
hc = 1.99 × 10
–25
 J•m = 1.24 × 10
3
 eV•nm
e
0
 = 8.85 × 10
–12
 C
2
/(N•m
2
)
k = 1/(4pe
0
) = 9.0 × 10
9
 (N•m
2
)/C
2
µ
0
 = 4p × 10
–7
 (T•m)/A
k' = µ
0
/(4p) = 1 × 10
–7
 (T•m)/A
1 atm = 1.0 × 10
5
 N/m
2
 = 1.0 × 10
5
 Pa
UNIT 
SYMBOLS
meter, m mole, mol watt, W farad, F
kilogram, kg hertz, Hz coulomb, C tesla, T
second, s newton, N volt, V degree Celsius, °C
ampere, A pascal, Pa ohm, ? electron volt, eV
kelvin, K joule, J henry, H
V ALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
? 0° 30° 37° 45° 53° 60° 90°
sin? 0 1/2 3/5 22 / 4/5 32 / 1
cos? 1 32 / 4/5 22 / 3/5 1/2 0
tan? 0 33 / 3/4 1 4/3 3 ¥
PREFIXES
Factor Prefix Symbol
10
9
giga G
10
6
mega M
10
3
kilo k
10
–2
centi c
10
–3
milli m
10
–6
micro µ
10
–9
nano n
10
–12
pico p
   
ADV ANCED PLACEMENT PHYSICS C TABLE OF INFORMATION
The following assumptions are used in this exam.
 I. The frame of reference of any problem is inertial unless otherwise 
stated.
 II. The direction of current is the direction in which positive charges 
would drift.
 III. The electric potential is zero at an infinite distance from an isolated 
point charge.
 IV . All batteries and meters are ideal unless otherwise stated.
 V . Edge effects for the electric field of a parallel plate capacitor are 
negligible unless otherwise stated.
GO ON TO THE NEXT PAGE.
Section I
   
MECHANICS ELECTRICITY AND MAGNETISM
v
x
 = v
x0
 + a
x
t
x = x
0
 + v
x0
t + 
1
2
a
x
t
2
vv ax x
xx x
2
0
2
0
2 =+ () -

 
a
F
m
F
m
net
==
S
F
dp
dt

 
=
JFdt p
 

==
?
?
??
pmv =

FF
fN
= µ
DEW Fdr == ·
?
?
?
K =
 
1
2
mv
2
P
dE
dt
=
PF v = ·
?
?
?U
g
 = mg?h
a
v
r
r
c
==
2
2
?
? ?
?
t× =rF
?
? ?
a
St t
==
II
net
Ir dm mr ==
?
22
S
x
mx
m
cm
ii
i
=
S
S
v = r?
?
?? ?
Lr pI == × ?
K =
 
1
2
I?
2
? = ?
0
 + at
? = ?
0
 + ?
0
t + 
1
2
at
2
a  =  acceleration
E  =  energy
F  =  force
f  =  frequency
h  =  height
I  =  rotational inertia
J  =  impulse
K  =  kinetic energy
k  =  spring constant
?  =  length
L  =  angular momentum
m  =  mass
P  =  power
p  =  momentum
r  =  radius or distance
T  =  period
t  =  time
U  =  potential energy
v  =  velocity or speed
W  =  work done on a system
x  =  position
µ  =  coefficient of friction
?  =  angle
t  =  torque
?  =  angular speed
a  =  angular acceleration
f  =  phase angle
?
?
Fk x
S
=- ?
U
S
 = 
1
2
k(?x)
2
x = x
max
cos(?t + f)
T
f
==
21 p
?
T
m
k
S
= 2p
T
g
P
= 2p
?
?
F
Gmm
r
G
=
12
2
U
Gmm
r
G
=
12
?
F
qq
r
E
=
1
4
0
12
2
pe
?
?
E
F
q
E
=
EdA
Q
·=
?
e
0
E
dV
dx
x
=-
?- VE dr = ·
?
  
V
q
r
i
i
i
=
?
1
4
0
pe
UqV
qq
r
E
==
1
4
0
12
pe
?V
Q
C
=
C
A
d
=
?e
0
CC
pi
i
=
?
11
CC
si
i
=
?
I
dQ
dt
=
U
C
 = 
1
2
Q?V = 
1
2
C(?V)
2
R
A
=
??
??
EJ = ?
I = Nev
d 
A
I
V
R
=
?
RR
si
i
=
?
11
RR
pi
i
=
?
P = I?V
A  =  area
B  =  magnetic field
C  =  capacitance
d  =  distance
E  =  electric field
e  =  emf
F  =  force
I  =  current
J  =  current density
L  =  inductance
?  =  length
n  =   number of loops of  
 wire per unit length
N  =   number of charge  
 carriers per unit  
 volume
P  =  power
Q  =  charge
q  =  point charge
R  =  resistance
r  =  radius or distance
t  =  time
U  =   potential or stored  
 energy
V  =  electric potential
v  =  velocity or speed
?  =  resistivity
F  =  flux
k  =  dielectric constant
?
?
?
FqvB
M
=×
Bd I ·=
?
µ
0
dB
Id r
r



=
µ
0
2
4p
× 
  
FIdB =
?
×
B
S
 = µ
0
nI
F
B
BdA =·
?
? ?
e-
F
=· =
?
Ed
d
dt
B
e- = L
dI
dt
U
L
 = 
1
2
LI
2
Page 4


AP Physics C: Electricity and Magnetism Practice Test 2
GO ON TO THE NEXT PAGE.
Section I
  
CONSTANTS AND CONVERSION FACTORS
Proton mass,
Neutron mass,
Electron mass,
Avogadro’s number,
Universal gas constant,
Boltzmann’s constant,
m
p
 = 1.67 × 10
–27
 kg
m
n
 = 1.67 × 10
–27
 kg
m
e
 = 9.11 × 10
–31
 kg
N
A
 = 6.02 × 10
23
 mol
–1
R = 8.31 J/(mol K)
k
B
 = 1.38 × 10
–23
 J/K
Electron charge magnitude,
1 electron volt,
Speed of light,
Universal gravitational constant,
Acceleration due to gravity 
at Earth’s surface,
e  = 1.60 × 10
–19
 C
1 eV = 1.60 × 10
–19
 J
c = 3.00 × 10
8
 m/s
G = 6.67 × 10
–11
 (N•m
2
)/kg
2
g = 9.8 m/s
2
1 unified atomic mass unit,
Planck’s constant,
Vacuum permittivity,
Coulomb’s law constant,
Vacuum permeability,
Magnetic constant,
1 atmosphere pressure,
1 u = 1.66 × 10
–27
 kg = 931 MeV/c
2
h = 6.63 × 10
–34
 J•s = 4.14 × 10
–15
 eV•s
hc = 1.99 × 10
–25
 J•m = 1.24 × 10
3
 eV•nm
e
0
 = 8.85 × 10
–12
 C
2
/(N•m
2
)
k = 1/(4pe
0
) = 9.0 × 10
9
 (N•m
2
)/C
2
µ
0
 = 4p × 10
–7
 (T•m)/A
k' = µ
0
/(4p) = 1 × 10
–7
 (T•m)/A
1 atm = 1.0 × 10
5
 N/m
2
 = 1.0 × 10
5
 Pa
UNIT 
SYMBOLS
meter, m mole, mol watt, W farad, F
kilogram, kg hertz, Hz coulomb, C tesla, T
second, s newton, N volt, V degree Celsius, °C
ampere, A pascal, Pa ohm, ? electron volt, eV
kelvin, K joule, J henry, H
V ALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
? 0° 30° 37° 45° 53° 60° 90°
sin? 0 1/2 3/5 22 / 4/5 32 / 1
cos? 1 32 / 4/5 22 / 3/5 1/2 0
tan? 0 33 / 3/4 1 4/3 3 ¥
PREFIXES
Factor Prefix Symbol
10
9
giga G
10
6
mega M
10
3
kilo k
10
–2
centi c
10
–3
milli m
10
–6
micro µ
10
–9
nano n
10
–12
pico p
   
ADV ANCED PLACEMENT PHYSICS C TABLE OF INFORMATION
The following assumptions are used in this exam.
 I. The frame of reference of any problem is inertial unless otherwise 
stated.
 II. The direction of current is the direction in which positive charges 
would drift.
 III. The electric potential is zero at an infinite distance from an isolated 
point charge.
 IV . All batteries and meters are ideal unless otherwise stated.
 V . Edge effects for the electric field of a parallel plate capacitor are 
negligible unless otherwise stated.
GO ON TO THE NEXT PAGE.
Section I
   
MECHANICS ELECTRICITY AND MAGNETISM
v
x
 = v
x0
 + a
x
t
x = x
0
 + v
x0
t + 
1
2
a
x
t
2
vv ax x
xx x
2
0
2
0
2 =+ () -

 
a
F
m
F
m
net
==
S
F
dp
dt

 
=
JFdt p
 

==
?
?
??
pmv =

FF
fN
= µ
DEW Fdr == ·
?
?
?
K =
 
1
2
mv
2
P
dE
dt
=
PF v = ·
?
?
?U
g
 = mg?h
a
v
r
r
c
==
2
2
?
? ?
?
t× =rF
?
? ?
a
St t
==
II
net
Ir dm mr ==
?
22
S
x
mx
m
cm
ii
i
=
S
S
v = r?
?
?? ?
Lr pI == × ?
K =
 
1
2
I?
2
? = ?
0
 + at
? = ?
0
 + ?
0
t + 
1
2
at
2
a  =  acceleration
E  =  energy
F  =  force
f  =  frequency
h  =  height
I  =  rotational inertia
J  =  impulse
K  =  kinetic energy
k  =  spring constant
?  =  length
L  =  angular momentum
m  =  mass
P  =  power
p  =  momentum
r  =  radius or distance
T  =  period
t  =  time
U  =  potential energy
v  =  velocity or speed
W  =  work done on a system
x  =  position
µ  =  coefficient of friction
?  =  angle
t  =  torque
?  =  angular speed
a  =  angular acceleration
f  =  phase angle
?
?
Fk x
S
=- ?
U
S
 = 
1
2
k(?x)
2
x = x
max
cos(?t + f)
T
f
==
21 p
?
T
m
k
S
= 2p
T
g
P
= 2p
?
?
F
Gmm
r
G
=
12
2
U
Gmm
r
G
=
12
?
F
qq
r
E
=
1
4
0
12
2
pe
?
?
E
F
q
E
=
EdA
Q
·=
?
e
0
E
dV
dx
x
=-
?- VE dr = ·
?
  
V
q
r
i
i
i
=
?
1
4
0
pe
UqV
qq
r
E
==
1
4
0
12
pe
?V
Q
C
=
C
A
d
=
?e
0
CC
pi
i
=
?
11
CC
si
i
=
?
I
dQ
dt
=
U
C
 = 
1
2
Q?V = 
1
2
C(?V)
2
R
A
=
??
??
EJ = ?
I = Nev
d 
A
I
V
R
=
?
RR
si
i
=
?
11
RR
pi
i
=
?
P = I?V
A  =  area
B  =  magnetic field
C  =  capacitance
d  =  distance
E  =  electric field
e  =  emf
F  =  force
I  =  current
J  =  current density
L  =  inductance
?  =  length
n  =   number of loops of  
 wire per unit length
N  =   number of charge  
 carriers per unit  
 volume
P  =  power
Q  =  charge
q  =  point charge
R  =  resistance
r  =  radius or distance
t  =  time
U  =   potential or stored  
 energy
V  =  electric potential
v  =  velocity or speed
?  =  resistivity
F  =  flux
k  =  dielectric constant
?
?
?
FqvB
M
=×
Bd I ·=
?
µ
0
dB
Id r
r



=
µ
0
2
4p
× 
  
FIdB =
?
×
B
S
 = µ
0
nI
F
B
BdA =·
?
? ?
e-
F
=· =
?
Ed
d
dt
B
e- = L
dI
dt
U
L
 = 
1
2
LI
2
GO ON TO THE NEXT PAGE.
Section I
  
GEOMETRY AND TRIGONOMETRY CALCULUS
Rectangle
A = bh
Triangle
A = 
1
2
bh
Circle
A = pr
2
C = 2pr
s = r?
Rectangular Solid
V = ?wh
Cylinder
V = pr
2
?
S = 2pr? + 2pr
2
Sphere
V =
 
4
3
pr
3
S = 4pr
2
Right Triangle
a
2
 + b
2
 = c
2
sin? = 
a
c
cos? = 
b
c
tan? = 
a
b
A  =  area
C  =  circumference
V  =  volume
S  =  surface area
b  =  base
h  =  height
?  =  length
w  =  width
r  =  radius
s  =  arc length
?  =  angle
df
dx
df
du
du
dx
=
d
dx
xnx
nn
()=
-1
d
dx
eae
ax ax
() =
d
dx
ax
x
(ln) =
1
d
dx
ax aax [sin()]cos() =
d
dx
ax aax [cos()]sin() =-
xdx
n
xn
nn
=
+
+
?
1
1
1
1
, ?-
edx
a
e
ax ax
=
?
1
dx
xa
xa
+
=+
?
ln
cos( )sin() ax dx
a
ax =
?
1
sin( )cos() ax dx
a
ax =
?
-
1
VECTOR PRODUCTS
? ?
AB AB ·= cos?
? ?
AB AB ×= sin?
r
x
?
c
b
a
90°
?
Page 5


AP Physics C: Electricity and Magnetism Practice Test 2
GO ON TO THE NEXT PAGE.
Section I
  
CONSTANTS AND CONVERSION FACTORS
Proton mass,
Neutron mass,
Electron mass,
Avogadro’s number,
Universal gas constant,
Boltzmann’s constant,
m
p
 = 1.67 × 10
–27
 kg
m
n
 = 1.67 × 10
–27
 kg
m
e
 = 9.11 × 10
–31
 kg
N
A
 = 6.02 × 10
23
 mol
–1
R = 8.31 J/(mol K)
k
B
 = 1.38 × 10
–23
 J/K
Electron charge magnitude,
1 electron volt,
Speed of light,
Universal gravitational constant,
Acceleration due to gravity 
at Earth’s surface,
e  = 1.60 × 10
–19
 C
1 eV = 1.60 × 10
–19
 J
c = 3.00 × 10
8
 m/s
G = 6.67 × 10
–11
 (N•m
2
)/kg
2
g = 9.8 m/s
2
1 unified atomic mass unit,
Planck’s constant,
Vacuum permittivity,
Coulomb’s law constant,
Vacuum permeability,
Magnetic constant,
1 atmosphere pressure,
1 u = 1.66 × 10
–27
 kg = 931 MeV/c
2
h = 6.63 × 10
–34
 J•s = 4.14 × 10
–15
 eV•s
hc = 1.99 × 10
–25
 J•m = 1.24 × 10
3
 eV•nm
e
0
 = 8.85 × 10
–12
 C
2
/(N•m
2
)
k = 1/(4pe
0
) = 9.0 × 10
9
 (N•m
2
)/C
2
µ
0
 = 4p × 10
–7
 (T•m)/A
k' = µ
0
/(4p) = 1 × 10
–7
 (T•m)/A
1 atm = 1.0 × 10
5
 N/m
2
 = 1.0 × 10
5
 Pa
UNIT 
SYMBOLS
meter, m mole, mol watt, W farad, F
kilogram, kg hertz, Hz coulomb, C tesla, T
second, s newton, N volt, V degree Celsius, °C
ampere, A pascal, Pa ohm, ? electron volt, eV
kelvin, K joule, J henry, H
V ALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
? 0° 30° 37° 45° 53° 60° 90°
sin? 0 1/2 3/5 22 / 4/5 32 / 1
cos? 1 32 / 4/5 22 / 3/5 1/2 0
tan? 0 33 / 3/4 1 4/3 3 ¥
PREFIXES
Factor Prefix Symbol
10
9
giga G
10
6
mega M
10
3
kilo k
10
–2
centi c
10
–3
milli m
10
–6
micro µ
10
–9
nano n
10
–12
pico p
   
ADV ANCED PLACEMENT PHYSICS C TABLE OF INFORMATION
The following assumptions are used in this exam.
 I. The frame of reference of any problem is inertial unless otherwise 
stated.
 II. The direction of current is the direction in which positive charges 
would drift.
 III. The electric potential is zero at an infinite distance from an isolated 
point charge.
 IV . All batteries and meters are ideal unless otherwise stated.
 V . Edge effects for the electric field of a parallel plate capacitor are 
negligible unless otherwise stated.
GO ON TO THE NEXT PAGE.
Section I
   
MECHANICS ELECTRICITY AND MAGNETISM
v
x
 = v
x0
 + a
x
t
x = x
0
 + v
x0
t + 
1
2
a
x
t
2
vv ax x
xx x
2
0
2
0
2 =+ () -

 
a
F
m
F
m
net
==
S
F
dp
dt

 
=
JFdt p
 

==
?
?
??
pmv =

FF
fN
= µ
DEW Fdr == ·
?
?
?
K =
 
1
2
mv
2
P
dE
dt
=
PF v = ·
?
?
?U
g
 = mg?h
a
v
r
r
c
==
2
2
?
? ?
?
t× =rF
?
? ?
a
St t
==
II
net
Ir dm mr ==
?
22
S
x
mx
m
cm
ii
i
=
S
S
v = r?
?
?? ?
Lr pI == × ?
K =
 
1
2
I?
2
? = ?
0
 + at
? = ?
0
 + ?
0
t + 
1
2
at
2
a  =  acceleration
E  =  energy
F  =  force
f  =  frequency
h  =  height
I  =  rotational inertia
J  =  impulse
K  =  kinetic energy
k  =  spring constant
?  =  length
L  =  angular momentum
m  =  mass
P  =  power
p  =  momentum
r  =  radius or distance
T  =  period
t  =  time
U  =  potential energy
v  =  velocity or speed
W  =  work done on a system
x  =  position
µ  =  coefficient of friction
?  =  angle
t  =  torque
?  =  angular speed
a  =  angular acceleration
f  =  phase angle
?
?
Fk x
S
=- ?
U
S
 = 
1
2
k(?x)
2
x = x
max
cos(?t + f)
T
f
==
21 p
?
T
m
k
S
= 2p
T
g
P
= 2p
?
?
F
Gmm
r
G
=
12
2
U
Gmm
r
G
=
12
?
F
qq
r
E
=
1
4
0
12
2
pe
?
?
E
F
q
E
=
EdA
Q
·=
?
e
0
E
dV
dx
x
=-
?- VE dr = ·
?
  
V
q
r
i
i
i
=
?
1
4
0
pe
UqV
qq
r
E
==
1
4
0
12
pe
?V
Q
C
=
C
A
d
=
?e
0
CC
pi
i
=
?
11
CC
si
i
=
?
I
dQ
dt
=
U
C
 = 
1
2
Q?V = 
1
2
C(?V)
2
R
A
=
??
??
EJ = ?
I = Nev
d 
A
I
V
R
=
?
RR
si
i
=
?
11
RR
pi
i
=
?
P = I?V
A  =  area
B  =  magnetic field
C  =  capacitance
d  =  distance
E  =  electric field
e  =  emf
F  =  force
I  =  current
J  =  current density
L  =  inductance
?  =  length
n  =   number of loops of  
 wire per unit length
N  =   number of charge  
 carriers per unit  
 volume
P  =  power
Q  =  charge
q  =  point charge
R  =  resistance
r  =  radius or distance
t  =  time
U  =   potential or stored  
 energy
V  =  electric potential
v  =  velocity or speed
?  =  resistivity
F  =  flux
k  =  dielectric constant
?
?
?
FqvB
M
=×
Bd I ·=
?
µ
0
dB
Id r
r



=
µ
0
2
4p
× 
  
FIdB =
?
×
B
S
 = µ
0
nI
F
B
BdA =·
?
? ?
e-
F
=· =
?
Ed
d
dt
B
e- = L
dI
dt
U
L
 = 
1
2
LI
2
GO ON TO THE NEXT PAGE.
Section I
  
GEOMETRY AND TRIGONOMETRY CALCULUS
Rectangle
A = bh
Triangle
A = 
1
2
bh
Circle
A = pr
2
C = 2pr
s = r?
Rectangular Solid
V = ?wh
Cylinder
V = pr
2
?
S = 2pr? + 2pr
2
Sphere
V =
 
4
3
pr
3
S = 4pr
2
Right Triangle
a
2
 + b
2
 = c
2
sin? = 
a
c
cos? = 
b
c
tan? = 
a
b
A  =  area
C  =  circumference
V  =  volume
S  =  surface area
b  =  base
h  =  height
?  =  length
w  =  width
r  =  radius
s  =  arc length
?  =  angle
df
dx
df
du
du
dx
=
d
dx
xnx
nn
()=
-1
d
dx
eae
ax ax
() =
d
dx
ax
x
(ln) =
1
d
dx
ax aax [sin()]cos() =
d
dx
ax aax [cos()]sin() =-
xdx
n
xn
nn
=
+
+
?
1
1
1
1
, ?-
edx
a
e
ax ax
=
?
1
dx
xa
xa
+
=+
?
ln
cos( )sin() ax dx
a
ax =
?
1
sin( )cos() ax dx
a
ax =
?
-
1
VECTOR PRODUCTS
? ?
AB AB ·= cos?
? ?
AB AB ×= sin?
r
x
?
c
b
a
90°
?
GO ON TO THE NEXT PAGE.
Section I
   
PHYSICS C: ELECTRICITY AND MAGNETISM 
SECTION I
Time—45 minutes
35 Questions
Directions: Each of the following questions or incomplete statements below is followed by five suggested answers or completions. 
Select the one that is best in each case and then mark it on your answer sheet.
 36. Three 3 µF capacitors are connected in parallel as shown 
above. Determine the equivalent capacitance of the ar-
rangement.
(A) 
1
3
µF
(B) 1 µF
(C) 3 µF
(D) 6 µF
(E) 9 µF
 37. A particular microwave requires some power, P, to oper-
ate. In America, a typical outlet provides electricity at 
120 V .  This would send a current, I, to the microwave. 
If this same microwave were taken to Europe, where the 
outlets provide twice the voltage, what would be the new 
current?
(A) 
1
4
I
(B)
 
1
2
I
(C) I
(D) 2I
(E) 4I
E
+2Q
 38. A uniform electric field exists in a region, and then a neu-
tral, conducting, spherical shell with a stationary charge 
+2Q at its center is placed in the region, as shown above. 
The radius of the sphere is R. The flux through the sphere 
depends on the value of
(A) E, Q, and R
(B) Only R
(C) E and Q 
(D) R and Q
(E) Only Q
 39. In a certain region, the electric field varies with the radius 
away from origin by the equation E
r
 = –6r
2 
+ 4r + 3, 
where r is given in meters and E in N/C. The potential 
difference between the origin and the point (3, 4) is 
(A) –165 V
(B) –120 V
(C)     64 V
(D)    185 V
(E)   315 V