1. Concept Questions
A wire, initially carrying no current, has a radius that starts decreasing at t = 0. As it shrinks, which way does current begin to flow in the loop?
A) Clockwise B) Counter-clockwise C) No current
D) Insufficient information
Calculate flux downwards – we get EMF clockwise
Flux is decreasing
Derivative of flux is negative
EMF is positive clockwise
Current will flow clockwise
Right hand rule – B-field downwards
Reinforces magnetic field
Tries to keep the B-flux constant
The current that flows will then create a magnetic field, which inside the loop, will
A) Strengthen it B) Weaken it C) No change D) Insufficient information

2. What if we used a superconductor?
Concept Question
What happens as I drop the magnet into the copper tube?
A) Falls as usual B) Falls slower
C) Falls faster D) Floats constant
E) Pops back up and out N S S N
As magnet falls, some places have magnetic fields that diminish
Current appears, replacing magnetic field
This acts like a magnet, pulling it back up
At bottom end, current appears to oppose change
This repels the magnet, slowing it down S N
Current is only caused by motion of magnet
If motion stops, resistance stops current
If motion is small, opposition will be small
It doesn’t stop, it goes slowly
What if we used a superconductor?

3. Concept Question What is Kirchoff’s law for the loop shown?
A) E + L (dI /dt) = 0 B) E – L (dI /dt) = 0
C) None of the above
D) I don’t know Kirchoff’s law for switches I + – L E
The voltage change for an inductor is L (dI/dt)
Negative if with the current
Positive if against the current

4. Concept Question
In the steady state, with the switch closed, how much current flows through R2? How much current flows through R2 the moment after we open the switch?
A) 0 A B) 6 A C) 3 A
D) 2 A E) None of the above
R2 = 4 
6 A
6 A
6 A L
R1 = 2  + –
E = 12 V
In the steady state, the inductor is like a wire
Both ends of R2 are at the same potential: no current through R2
The remaining structure had current I = E/R1 = 6 A running through it
I = E /R1 = 6 A
Now open the switch – what happens?
Inductors resist changes in current, so the current instantaneously is unchanged in inductor
It must pass through R2
I = 6 A

5. Loop has unin-tended inductance
Concept Question
The circuit at right is in a steady state. What will the voltmeter read as soon as the switch is opened?
A) 0.l V B) 1 V C) 10 V
D) 100 V E) 1000 V
R1 = 10  L
I = 1 A V
R2 = 1 k + –
E = 10 V
The current remains constant at 1 A
It must pass through resistor R2
The voltage is given by V = IR
Note that inductors can produce very high voltages
Inductance causes sparks to jump when you turn a switch off + –
Loop has unin-tended inductance

6. Energy sloshes back and forth
Concept Question
A capacitor with charge on it has energy U = Q2/2C, but Q is constantly changing. Where does the energy go?
A) It is lost in the resistance of the wire
B) It is stored as kinetic energy of the electrons
C) It is stored in the inductor
D) Hollywood! I Q C L
Let’s find the energy in the capacitor and the inductor
Energy sloshes back and forth

7. Concept Question
If the voltage from a source looks like the graph below, about what voltage should it be labeled?
0 V B) 170 V C) 120 V D) 85 V
E) It should be labeled some other way
Average voltage is zero, but that doesn’t tell us anything
Maximum voltage 170 V is an overstatement
Power is usually proportional to voltage squared

8. Concept Question
A 60 W light bulb is plugged into a standard outlet (Vrms = 120 V). What is the resistance of the bulb?
A) 15  B) 30  C) 60 
D) 120  E) 240 

9. Capacitors and Resistors Combined
Capacitors and resistors both limit the current – they both have impedance
Resistors: same impedance at all frequencies
Capacitors: more impedance at low frequencies
Concept Question
The circuit at right might be designed to:
Let low frequencies through, but block high frequencies
Let high frequencies through, but block low frequencies
Let small currents through, but not big currents
Let big currents through, but not small currents

10. Impedance Table Resistor Capacitor Inductor Impedance R Phase
Vector Direction
right
down up
Inductors are good for
Blocking low frequencies
Blocking high frequencies
Blocking large currents
Blocking small currents

11. Concept Question
In the mystery box at right, we can put a 2.0 F capacitor, a 4.0 H inductor, or both (in series). Which one will cause the greatest current to flow through the circuit?
A) The capacitor B) The inductor C) both
D) Insufficient information
1.4 k ?
60 Hz 170 V
2.0 F
We want to minimize impedance
Make the vector sum as short as possible
Recall, capacitors point down, inductors up
The sum is shorter than either separately
L= 4.0 H
1.3 k
1.5 k
1.4 k

12. Concept Question L C R f Vmax
How will XL and XC compare at the frequency where the maximum power is delivered to the resistor?
A) XL > XC B) XL < XC C) XL = XC D) Insufficient information
Resonance happens when XL = XC.
This makes Z the smallest
It happens only at one frequency
Same frequency we got for LC circuit

13. Concept Question
In the example we just did, we found only some frequencies get through
What happens if this is impossible to meet, because 1/RC > R/L?
A) The inequality gets reversed, R/L <  < 1/RC
B) Pretty much everything gets blocked
C) Only a very narrow frequency range gets through C L R f
Vmax = 5 V

14. Concept Question Voltage
When the voltage shown in blue was passed through two components in series, the current shown in red resulted. What two components might they be?
A) Capacitor and Inductor
B) Inductor and Resistor
C) Capacitor and Resistor
Current
The phase shift represents how the timing of the current compares to the timing of the voltage
When it is positive, the current lags the voltage
It rises/falls/peaks later
When it is negative, the current leads the voltage
It rises/falls/peaks earlier

15. Concept Question
A transformer has 10,000 V AC going into it, and it is supposed to produce 120 V AC, suitable for household use. If the primary winding has 5,000 turns, how many should the secondary have?
A) 120 B) 240 C) 60
D) None of the above
N1 =5000
N2 =?
V1 = 10 kV
V2 = 120 V

16. Concept Question A wave has an electric field given by
What does the magnetic field look like?
A) B)
C) D)
The magnitude of the wave is B0 = E0 / c
The wave is traveling in the z-direction, because of sin(kz - t).
The wave must be perpendicular to the E-field, so perpendicular to j
The wave must be perpendicular to direction of motion, to k
It must be in either +i direction or –i direction
If in +i direction, then E  B would be in direction j  i = - k, wrong
So it had better be in the –i direction

17. Concept Question Radio Waves Microwaves Red Infrared Orange
Which of the following waves has the highest speed in vacuum?
A) Infrared
B) Orange
C) Green
D) It’s a tie
E) Not enough info
Radio Waves
Microwaves
Infrared
Visible
Ultraviolet
X-rays
Gamma Rays
f Increasing
 Increasing
Red
Orange
Yellow
Green
Blue
Violet

18. Cross-Section
To calculate the power falling on an object, all that matters is the light that hits it
Example, a rectangle parallel to the light feels no pressure
Ask yourself: what area does the light see?
This is called the cross section
If light of intensity S hits an absorbing sphere of radius a, what is the force on that sphere?
A) a2S/c B) 2a2S/c C) 4a2S/c
As viewed from any side, a sphere looks like a circle of radius a
The cross section for a sphere, then, is a2

19. End of material for Test 3
Equations for Test 3
Faraday’s Law
Transformers:
Power and Pressure
Impedance:
Inductors:
Units:
Frequency, Wavelength
Speed of Light
End of material for Test 3