FINAL EXAM PHYS 121
VERSION C
SUMMER 2003
________________________________________________________________________________________________
The exam is closed book and closed notes.
e=1.6x10-19 C me=9.11x10-31kg k = 8.99x109 Nm2/C2
F=k
q 1q 2
;
r2
i
q1
; Area = r2
r2

0 A
d
C
dQ
dt
J
0 A
d
i
A
C
R
F = qE
E
q
  EdA  encl
0
Q

A
C
E=k
V
i
k=

2 0
Q
V
R
0 = 8.85x10-12 C2/ Nm2 ; 0 = 1.26x10-6 Tm/A
1 m = 1000 mm
E
U
L
A
1
4  0

20 r
1 m = 100 cm

V   E  ds
Q2
1
 C  V  CV 2
2C
2
E
E
1 mega (1M ) = 106
V
d
 1
1
1 
series : Ceq   
 ... 
Cn 
 C1 C2
V
d
1
parallel: Ceq = C1+C2+…Cn
U = -W = qV
parallel : R eq
j = (ne) vd
V = - Ed
 1
1
1
 

 ...
Rn
 R1 R 2
j = i/A E = J




point charge, sphere: V = k
Q = Q0 e-t/RC,
F = qvxB
F = iLxB
Bstraight wire = 0I/2R
 - 0 = 0(T - T0)
XL = L
XC = 1/C
Z  R  (X L  X C )
2
Vc = V0 (e-t/RC),
Bloop = 0I/2R
emfsel-induced = -Ldi/dt
Vrms 
Vmax
2
VR = i0 R (e-t/RC),
VR = i0 R (e-t/RC),
 = xB
 = NiA
Bsem = 0I/4R Bsolenoid = 0In
0 = 1.26x10-6 Tm/A
emfmax = NABAC circuit: emf = Emsint
Im = Vm/Z tan = (XL - XC))/R
2
P = i2R = V2/R series: Req = R1 + R2+..Rn
i = i0 (e-t/RC),
qvxB = mv2/R
v = E/B
Barc = 0I/4R
P = iV
VC = V (1-e-t/RC),
i = i0 (e-t/RC),
Flux:  = BA emf = -d/dt
charged plane: V = V0 - Ex
1
RC-circuit: charging: Q = Q0(1-e-t/RC),
discharging:
q1
r
I rms 
Pavg = IrmsVrmscos
I max
0 
2
1. Two point charges are arranged as shown. In which region could a third charge
+2 C be placed so that the net electrostatic force on it is zero?
A)
I only
B)
I and II only
C)
III only
D)
I and III only
E)
II only
1
LC
I = Im sin(t-)
cos = R/Z
2. A 5-nC charge is placed at the origin, a 6 -nC charge is placed 0.3 m from the origin on the x
axis, and a third -3-nC charge is placed 0.1 m from the origin on the y axis. The magnitude of the
force on the charge at the origin is
A. 0.13x10-6 N
B. 0.34x10-6 N
C. 5.68x10-6 N
D. 8.90x10-6 N
E. 13.8x10-6 N
3. A spherical conducting shell has charge q=6pC. An insulating sphere with uniformly
distributed charge Q=23pC is placed at the center of the cavity. Calculate the magnitude of
the electric field 30 cm from the center.
A. 1.00 N/C
B. 2.50 N/C
C. 3.00 N/C
D. 4.50 N/C
E. 5.00 N/C
4. Two identical charges of opposite sign are located on a horizontal axis. If a = 20 cm , d = 2a and q
= 3 nC, what is the electric potential at P on a vertical axis as shown in the figure?
A. 184 V
B. 130 V
C. 60V
D. 24 V
E. 0
5. An electron moves from point i to point f, in the direction of a uniform electric field. During this
placement:
A. the work done by the field is positive and the potential energy of the electron-field system increases
B. the work done by the field is negative and the potential energy of the electron-field system increases
C. the work done by the field is positive and the potential energy of the electron-field system decreases
D. the work done by the field is negative and the potential energy of the electron-field system decreases
E. the work done by the field is positive and the potential energy of the electron-field system does not change
6. An electron is accelerated from rest through a potential difference of 2500 V. What is its final velocity?
A. 8x107 m/s
B. 3x107 m/s
C. 5x106 m/s
D. 8x105 m/s
E. 7x104 m/s
7. In the circuit shown capacitor C1=16 nF is first charged by closing of switch S1 and
connecting it to battery of V = 30 V. Switch S1 is then opened, and charged capacitor is
connected to the uncharged capacitor by closing switch S2. The potential difference across
capacitor drops to 20 V. What is the capacitance of capacitor C2 ?
A. 10 nF
B. 20 nF
C. 30 nF
D. 8 nF
E. 50 nF
8. What is the equivalent capacitance between terminal A and B for the following circuit?
A. 7.5 nF
B. 32 nF
C. 40 nF
D. 70 nF
E. 92 nF
9. What maximum potential difference (before it breaks down) can be applied to an air filled parallel-plate capacitor C = 2 nF
if the surface area is 8x10 -4 m2? (dielectric strength of air is E = 3x106 V/m)
A. 2 V
B. 5 V
C. 7 V
D. 11V
E. 15 V
10. A 10-m long aluminum wire with a radius of 0.4 mm carries a current of 5 A. If resistivity of aluminum is 2.75x10 -8 m.
what is the potential difference across this wire?
A. 2.7 V
B. 8.6 V
C. 12.5 V
D. 18.2 V
E. 23.4 V
11. Two wires made of the same material have the same length but different diameter. They are connected in parallel to a
battery. The quantity that is NOT the same for the wires is:
A)
the end-to-end potential difference
B)
the current
C)
the current density
D)
the electric field
E)
the electron drift velocity
12.
A 120-V power line is protected by a 15-A fuse. What is the maximum number of "120 V, 500 W" light bulbs that can
be operated at full brightness from this line?
A)
1
B)
2
C)
3
D)
4
E)
5
13.
A.
B.
C.
D.
E.
For the circuit shown find the voltage across the 8- resistor.
25 V
40 V
67.5 V
80 V
700 V
14. What is the magnitude of the current through the R3 = 8  resistor if E = 15 V,
R1 = 5 , R2 = 20  and R3 = 8 
A. 0.01 A
B. 0.33 A
C. 0.71 A
D. 1 A
E. 1.5 A
15. For the RC circuit shown ( R = 1M, C = 5 F and  = 30 V) find the potential
difference across the capacitor 8 sec after the switch is closed.
A. 24 V
B. 15 V
C. 3.0 V
D. 1.5 V
E. 0.8 V
16. A positive particle (a proton) with charge 1.6.10-19C is moving with a velocity v=2.105 m/s in
the positive z direction. A magnetic field B = 125.10-3 T (kilo teslas) is pointing in the positive y
direction . Find the force acting on the particle.
A. 4 x 10-15 N, in the positive x-direction
B. 4 x 10-15 N, in the negative x-direction
C. 1.6 x 10-19 N, in the positive z-direction
D. 1.6 x 10-19 N, in the negative z-direction
E. zero
17. Two parallel wires carry currents of I1 = 20 - A and I2 = 10 -A, respectively, in the opposite
direction and have length of 5 m each. The distance between wires is d = 1 cm. Find the force
between the wires.
A. zero
B. 0.01 N, attraction
C. 0.01 N, repulsion
D. 0.02 N, attraction
E. 0.02 N, repulsion
18. Two long, straight wires are parallel and carry the same current of i1 = i2 = 6 A in the opposite direction as shown. If the
distance between the wires is 6 cm, and the distance from wire 1 to point B is 2 cm what are the direction and the magnitude
of the net magnetic field at point B seen in fig.
A. 4.5x10-5 T into the page
B. 8.0x10-5 T into the page
C. 1.6x10-4 T out of the page
D. 2.0x10 -4T into the page
E. 8.0x10-3 T out of the page
19. The two semicircular arcs AD and HD of radii R1 =8 cm and R2 = 5 cm respectively, form part
of the circuit carrying current of I = 2 A. Find the magnetic field produced by those arcs at C.
A. 81.0 µT
B. 44.2 µT
C. 20.5 µT
D. 7.2 µT
E. 4.7 µT
20. A uniform magnetic is normal to the plane of circular loop of wire, 12 cm in radius and of 0.05  resistance. At what rate
must the magnetic field change with time if an induced current of 0.2 A is to appear in the loop?
A.0.22 T/s
B. 3.42 T/s
C. 4.76 T/s
D. 24.5 T/s
E. 88.5 T/s
21. Two circular coils of equal radius 2 cm are placed several centimeters apart. If viewed from
left, the current in the closer loop is clockwise and decreasing with time at a constant rate. Describe
the direction of the current in the furthest loop.
A. clockwise
B. counterclockwise
C. oscillating
D. zero
E. depends on the distance between coils
22. A 240 V alternating source at 60 cycle is connected to a series RLC circuit with following values:
R=75 , L=120 mH, and C=12µF. The total impedance of the circuit is?
A. 100 
B. 142 
C. 191 
D. 245 
E. 300 
23. A series RLC circuit driven by an AC voltage contains reactances XL = 20  and XC = 14  and resistance R = 10.
What is the impedance at resonant frequency?
A. 10 
B. 14 
C. 20 
D. 24 
E. 30 
Resistance R = 100 , inductance L = 0.005 H, and capacitance C = 0.5 F are connected in series
with an ac generator with the alternating emf E = 10sin(6500t).
24.
A)
B)
C)
D)
E)
Find the impedance of the circuit.
300
600
1200
1500
1800
25.
A)
B)
C)
D)
E)
Find the current in the circuit (magnitude and phase). (I in mA,  in degrees)
4.2.sin(6500t-80)
6.sin(6500t-70)
12.sin(6500t-80)
15.sin(6500t-70)
34.sin(6500t+70)
26.
A)
B)
C)
D)
E)
Find the maximum potential across the inductance (V)
1.1
4.2
5.6
6.7
8.0
27.
A)
Find the resonant frequency. (in Hz, closest)
600
B)
C)
D)
E)
1200
2500
3200
5400
28. Find the power dissipated in the circuit.
A.
B.
C.
D.
E.
10 mW
28 mW
58 mW
62 mW
128 mW
A 3F capacitor, previously charged by the 12 V battery, was connected across 5 mH inductor.
29. The frequency of the oscillations is closest to:
A. 1000 Hz
B. 3000 Hz
C. 4000 Hz
D. 5000 Hz
E. 6000 Hz
30. Find the maximum value of current in the circuit?
A. 0.05 A
B. 0.1 A
C. 0.15 A
D. 0.20 A
E. 0.25 A