### Fall 2008 Physics 212 Hour Exam 3(27 questions)

The grading button and a description of the scoring criteria are at the bottom of this page. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

True-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 127. The exam period was 90 minutes; the average score was 99.6; the median score was 102. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1**

This and the next two questions refer to this RLC circuit: At what frequency, f (= ω/2π) is Irms maximum?

(a)   0 Hz
(b)   3.55 × 10-5 Hz
(c)   712 Hz
(d)   4.47 × 103 Hz
(e)   3.18 × 106 Hz

### QUESTION 2**

Fill in the blank: the current through the capacitor ______ the voltage across the resistor.

(b)   lags
(c)   is in phase with

### QUESTION 3**

The above circuit, with a variable capacitor, is used in your radio. Station 1 and station 2 emit at frequencies separated by 0.2 MHz. You have trouble receiving one station without getting pickup from the other. One way to get better discrimination would be to decrease the resistance R in the circuit.

(T)   True
(F)   False

### QUESTION 4**

A 4 μF capacitor is connected to a 16 mH inductor to form the LC circuit shown. There is no resistance in the circuit. At t = 0, the electric energy stored in the capacitor is equal to the magnetic energy stored in the inductor: UC = UL = 2 mJ, the current I is positive, and the charge Q on the top plate of the capacitor is positive. We note ω0 = 1/sqrt(LC) . What is the maximum current in the circuit?

(a)   IMAX = 1.00 A
(b)   IMAX = 0.71 A
(c)   IMAX = 0.50 A
(d)   IMAX = 0.35 A
(e)   IMAX = 0.25 A

### QUESTION 5*

An LRC circuit and its associated phasors are shown below.  Is the angular frequency ω greater than, less than, or equal to ωo, the resonant frequency?

(a)   ω > ωo
(b)   ω < ωo
(c)   ω = ωo

### QUESTION 6*

This and the next question refer to this situation:

An AC voltage source with angular frequency ω = 100 rad/s and root-mean-square voltage Erms = 110 V drives an RLC circuit.

What is the RMS current flowing in the circuit? (a)   Irms = 0.8 A
(b)   Irms = 1.9 A
(c)   Irms = 2.7 A
(d)   Irms = 8.2 A
(e)   Irms = 11.0 A

### QUESTION 7*

If the frequency is doubled how will Irms change ?

(a)   Irms will decrease.
(b)   Irms will remain the same.
(c)   Irms will increase.

### QUESTION 8** An ideal transformer with N1 turns in the primary coil and N2 turns in the secondary coil is connected to a voltage generator and a resistor as shown below. The generator EMF is given by ε sin(ωt). What is the peak power that the generator delivers during each cycle?

(a)
(b)
(c)
(d)
(e)

### QUESTION 9** A long solenoid has 500 turns, a diameter d = 1 cm and an inductance L = 2 × 10-6 H. If 0.5 amps of current flows through the solenoid, what is the magnetic field inside it?

(a)   B = 8.10 × 10-6 T
(b)   B = 1.42 × 10-5 T
(c)   B = 2.55 × 10-5 T

### QUESTION 10*

This and the next two questions refer to the diagram below:

Unpolarized light travels along the positive z-axis and passes through two ideal, linear polarizers with transmission axes (TA) shown as arrows in the below figure. The TA of the first polarizer is inclined at an angle Φ with respect to the x-axis, while the TA of the second polarizer is aligned along the y-axis. In Region #1 (before striking the 1st linear polarizer), the intensity is I1. In Region #2 (between the 1st and 2nd linear polarizer) the intensity is I2. In Region #3 (after the 2nd linear polarizer) the intensity is I3. The electric field in Region #2 is given by:

E = 0.8 E2 x cos (kz-ωt) + 0.6 E2 y cos (kz-ωt) Find the intensity ratio I2 / I1.

(a)   I2 / I1 = 0.80
(b)   I2 / I1 = 0.71
(c)   I2 / I1 = 0.64
(d)   I2 / I1 = 0.50
(e)   I2 / I1 = 0.36

### QUESTION 11*

Find the intensity ratio I3 / I2.

(a)   I3 / I2 = 0.80
(b)   I3 / I2 = 0.71
(c)   I3 / I2 = 0.64
(d)   I3 / I2 = 0.50
(e)   I3 / I2 = 0.36

### QUESTION 12**

If the TA of the second polarizer were oriented along the x-axis rather than along the y-axis, the ratio I3 / I2 would increase.

(T)   True
(F)   False

### QUESTION 13*

This and the next two questions refer to this situation:

Light traveling in diamond is incident on a 3 cm thick piece of sapphire. It enters the sapphire at an angle of 50° as shown. When it reaches a third material, it undergoes total internal reflection.

What is the incident angle θ1 of the light in the diamond?  (a)   θ1 = 24°
(b)   θ1 = 34°
(c)   θ1 = 44°
(d)   θ1 = 54°
(e)   θ1 = 64°

### QUESTION 14*

What is the horizontal distance x the light travels in the sapphire?

(a)   x = 6.4 cm
(b)   x = 7.2 cm
(c)   x = 8.6 cm
(d)   x = 9.3 cm
(e)   x = 12.1 cm

### QUESTION 15**

Which one of the following could be the third material?

(a)   ice only
(b)   fluorite only
(c)   titanium dioxide
(d)   either ice or fluorite
(e)   none of the above

### QUESTION 16* Light traveling through air (n = 1) is incident on a stack of four optical bricks at an incident angle of 15° as shown. What is the angle of the light beam in the fourth material?

(a)   θ = 12.5°
(b)   θ = 13.6°
(c)   θ = 15.2°

### QUESTION 17**

This and the next three questions concern the following situation: An electromagnetic plane wave is propagating in empty space. The electric field at time t = 0 over two wavelengths is sketched in the figure above. The E-field is given by E(x,y,z,t) = i E0 sin(kz+ωt). Here, i is the unit vector in the +x direction, j is the unit vector in the +y direction, and k is the unit vector in the +z direction.

Which one of the following expressions describes the magnetic field of this electromagnetic wave?

(a)   B(x,y,z,t) = i B0 sin(kz+ωt)
(b)   B(x,y,z,t) = j B0 sin(kz+ωt)
(c)   B(x,y,z,t) = k B0 cos(kz+ωt)
(d)   B(x,y,z,t) = -j B0 sin(kz+ωt)
(e)   B(x,y,z,t) = -i B0 cos(kz+ωt)

### QUESTION 18*

If the average intensity of the wave is 1 watt/m2, what is the average energy per unit volume <u> of the wave?

(a)   <u> = 0.67 × 10-9 J/m3
(b)   <u> = 1.23 × 10-9 J/m3
(c)   <u> = 1.90 × 10-9 J/m3
(d)   <u> = 2.82 × 10-9 J/m3
(e)   <u> = 3.33 × 10-9 J/m3

### QUESTION 19*

If the average intensity of the wave is 1 watt/m2, what is the peak value of the magnetic field Bo of the wave?

(a)   Bo = 7.28 × 10-9 tesla
(b)   Bo = 3.05 × 10-8 tesla
(c)   Bo = 7.58 × 10-8 tesla
(d)   Bo = 9.15 × 10-8 tesla
(e)   Bo = 1.53 × 10-7 tesla

### QUESTION 20**

If the angular frequency ω of the wave were doubled, what would be the new value of the wavelength λ ?

(a)   It would be one half its previous value.
(b)   It would be equal to its previous value.
(c)   It would be twice its previous value.

### QUESTION 21*

A plane electromagnetic wave travels in the +x direction. The electric field points along the y-axis and the magnetic field along the z-axis. The diagram below represents a "snapshot" of the plane wave at an instant in time. In the diagram, points 1, 2 and 3 all lie in the x-y plane. At the instant shown, which one of the following statements best describes the relative magnitudes of the magnetic field at points 1, 2, and 3? (a)   B2 > B1 > B3 = 0
(b)   B2 > B1 = B3 > 0
(c)    B2 > B1 = B3 = 0

### QUESTION 22*

This and the next two questions concern the following situation:

A parallel plate capacitor is charging with time. The current is flowing in the wires as shown in the figure. Point P lies a distance r from the wire to the left of the capacitor, and point Q lies between the capacitor plates the same distance r from the center of the capacitor. r is less that the radius of the capacitor plates. Let BP be the magnetic field at point P and let BQ and EQ be the magnetic and electric fields at point Q. While the capacitor is charging, which of the following statements is true?

(a)   BP ≠ 0, BQ = 0, EQ = 0
(b)   BP = 0, BQ ≠ 0, EQ = 0
(c)   BP = 0, BQ ≠ 0, EQ ≠ 0
(d)   BP ≠ 0, BQ = 0, EQ ≠ 0
(e)   BP ≠ 0, BQ ≠ 0, EQ ≠ 0

### QUESTION 23**

While the capacitor is charging, which one of the following statements is true?

(a)   | BP |  <  | BQ |
(b)   | BP |  =  | BQ |
(c)   | BP |  >  | BQ |

### QUESTION 24**

After a long time the capacitor is fully charged and dQ/dt is zero everywhere. Which statement is now true?

(a)   BQ = 0, EQ = 0
(b)   BQ ≠ 0, EQ = 0
(c)   BQ = 0, EQ ≠ 0

### QUESTION 25*

This and the next two questions concern the following situation:

The circuit shown below consists of a 9 V battery, three resistors, an ideal inductor and a switch. Assume that the switch has been open for a long time. The switch is now closed at t = 0. Immediately afterwards, what is the current I3 flowing through resistor R3?

(a)   10.2 mA
(b)   25.0 mA
(c)   34.6 mA
(d)   50.0 mA
(e)   150.0 mA

### QUESTION 26*

A very long time after the switch has been closed, what is the current I1 through R1?

(a)   10.2 mA
(b)   25.0 mA
(c)   34.6 mA
(d)   50.0 mA
(e)   150.0 mA

### QUESTION 27*

The switch is now suddenly opened. How long after opening the switch does it take for the current through the inductor to reach 1/e of its value just before the switch is opened?

(a)   4.3 μsec
(b)   10.6 μsec
(c)   20.0 μsec
(d)   34.8 μsec
(e)   60.0 μsec

Scoring of True-False (T,F) Questions:
• If you mark the correct answer, you get 2 points.
• If you mark the wrong answer or if you mark neither answer, you get 0 points.
Scoring of Multiple Choice I (a,b,c) Questions:
• If you mark the correct answer, you get 3 points.
• If you mark a wrong answer or if you mark none of the answers, you get 0 points.
Scoring of Multiple Choice II (a,b,c,d,e) Questions:
• If you mark one answer and it is the correct answer, you get 6 points.
• If you mark two answers and one of them is the correct answer, you get 3 points.
• If you mark three answers and one of them is the correct answer, you get 2 points.
• If you do not mark the correct answer, or if you mark more than three answers, or if you mark none of the answers, you get 0 points.