Name _________________
Test 3
April 11, 2012
This test consists of three parts. Please note that in parts II and III,
Constant
you can skip one question of those offered.
0  4 107 T  m/A
RL
Circuits
LC Circuits
Possibly useful formulas:
 L R
AC Circuits
  1 LC
I  I 0 e t 
V  Vmax sin t 
Q  Q0 cos t 
EM waves

I  I max sin t   
E0  cB0
I  1  e t  
R
Impedance
1
S  E  B
X C  1 C , X L  L
RMS values
0
RLC Circuits
2
2
2
V
Z  R   X L  XC 
Vrms  max
S  cB02 20
1
R2
2


  tan 1  X L  X C  R 
LC 4 L2
P S c
I
I rms  max
Q  Q0 e  Rt 2 L cos t 
0  1 LC
2
Inductor
L  0 N 2 A 
U  12 LI 2
Circles
C  2 R
A   R2
Generator
  N  BA sin t 
Triangles
A  12 BH
Spheres
A  4 R 2
V  43  R 3
Faraday’s Law
d
 E  ds   dt B
Cylinders
V   R2 L
Alat  2 RL
Ampere’s Law
 B  ds   I   
0
0
Cones
V   R2 L
1
3
Alat   R L2  R 2
Part I: Multiple Choice [20 points]
For each question, choose the best answer (2 points each)
1. In the simple circuit illustrated at right, at what frequencies will
the most power be transferred to the resistor?
A) Low frequencies
B) High frequencies
C) A broad range of intermediate frequencies
D) A narrow band of intermediate frequencies
E) Insufficient information
2. Electricity is produced in commercial generators by
A) Giant banks of chemical batteries
B) Extracting electrons from atoms and pumping them into wires
C) Rubbing objects together to produce static charges
D) Moving loops of wire near magnetic fields (or vice versa)
E) Accelerating electrons using light waves
0
dE
dt
3. If an electromagnetic wave has frequency f = 2 Hz, what is the angular frequency ?
B) 2 s-1
C) 42 s-1
D) 1/(2) s E) 1/(42) s
A) 1 s-1
4. Which two components work best if you want to create an oscillator?
A) Inductor and capacitor
B) Inductor and resistor
C) Resistor and capacitor
D) Inductor and diode
E) Capacitor and diode
5. If you put power into an RLC circuit, the power gradually drains away. Which
component is actually consuming the power?
A) The resistor (only)
B) The capacitor (only)
C) The inductor (only)
D) The capacitor and the resistor
E) The inductor and the resistor
6. Which of the following types of electromagnetic radiation moves fastest in vacuum?
A) Infrared
B) Radio C) X-rays
D) Gamma rays E) None; it is a tie
7. In an LC circuit, where is most of the energy stored at any given time?
A) In the capacitor
B) In the inductor
C) It is split evenly at all times, with 50% in each component
D) It is constantly being passed back and forth between the two components
E) It is impossible to answer this question without know the capacitance and/or the
inductance
8. Why do we use step-up transformers to increase the voltage very high before we
transport it across the country?
A) It has to go to many customers who each get just a little bit of this voltage
B) Some customers (like industry) require very high voltage
C) Since power is voltage by current, it vastly increases the power being transmitted
D) High voltage is less dangerous, so it is just a safety consideration
E) Since it is at high voltage, there is much less current needed, which decreases the
losses in transmission
9. A resistor with resistance R = 3  is connected in series to a capacitor with
impedance XC = 4 . What is the total impedance?
B) 4 
C) 5 
D) 7 
E) 25 
A) 1 
10. Which of the following is the correct relation between the wavelength  and wave
number k?
B)  k  2 C) 2 k  1 D)   2 k E) k  2
A)  k  1
Part II: Short answer [20 points]
Choose two of the following questions and give a short answer (1-3 sentences).
11. Explain qualitatively Lenz’s Law. Suppose I took a superconducting loop of wire out
of a region of magnetic field. What does Lenz’s Law tell us in this case?
12. The graph at right shows the
current (dashed curve) that
results from putting an AC
voltage (solid curve) through
a single component (resistor,
capacitor, inductor). Identify
which one, and explain how
you can tell.
13. Place the following in order from highest frequency to lowest: blue, green, orange,
red, violet, yellow. You may include additional colors if you wish, but you don’t get
extra credit..
Part III: Calculation: [60 points]
Choose three of the following four questions and perform the indicated
calculations (20 points each)
14. In 2187, a spaceship approaches neutron star EC50 which
has a magnetic field of 1.53×107 T and rotates 12.0 times
per second. The captain then places a circular loop of
wire of radius 500 m with 12 turns in it in the vicinity of
this magnetic field, so at t = 0, the magnetic field is
perpendicular to the loop.
(a) Find the magnetic flux through the loop at t = 0.
magnetic field
Wire
loop
EC50
magnetic field
(b) Half a cycle later, the neutron star has rotated, so that the field is now reversed.
What is the flux now? What time is it now?
(c) Assume the magnetic field changed linearly between part (a) and part (b). What
was the EMF generated in the loop of wire during this half-rotation?
5A
1.50 k 
4.0 H
15. A 4.0 H inductor and a 1.50 k resistor are connected as
shown at right, and 5.0 A of current is then fed through it
until it attains a steady state. Assume the inductor has no
resistance.
(a) In a steady state, how much current flows through the
inductor? The resistor?
5A
(b) At t = 0, the external current is suddenly switched off. What is the current
through the inductor and resistor a moment later? What is the voltage across the
resistor at this moment?
(c) How long will it take until the current in the inductor has dropped to 0.0010 A?
16. A certain device requires AC voltage Vmax  5.00 V , with a maximum current
I max  1.40 A , but all that is available is house current with Vrms  120 V .
(a) What is the rms voltage and current required by the device?
(b) A transformer with 50 turns on the secondary (output) side will be used to supply
this current. How many turns should there be on the primary (input) side of the
transformer? Assume the transformer is 100% efficient.
(c) What will be the rms current drawn from the primary source?
8.0 m
(b) What is the total momentum transferred to the spacecraft by the light beam?
6.0 m
directly at the spaceship’s pointy end for a duration of
1.00 hour.
(a) What is the maximum intensity of the magnetic
field and electric field from this wave?
6.0 m
17. A black spaceship in the shape of a cone with radius
6.0 m and height 8.0 m is being impacted by a light
beam with intensity S  5.00 108 W/m 2 beamed