### Fall 2009 Physics 212 Hour Exam 3(25 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 109. The exam period was 90 minutes; the average score was 70.5; the median score was 71. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

This and the next two questions concern the following situation:

Consider the following arrangement of 4 polarizers. The first has a horizontal transmission axis, the second is oriented at 30° with respect to the horizontal, the third at 60° to the horizontal, and the fourth at 90° to the horizontal. The light incident on the first polarizer from the left is unpolarized.

The ratio of the final intensity of the transmitted light to the intensity of the incident light is:

(a)   0.65
(b)   0.32
(c)   0.2

### QUESTION 2*

If the third and fourth polarizers are interchanged, the final intensity of the transmitted light will

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

### QUESTION 3**

Let's start with the original situation as described in question 1 above. If the first polarizer is replaced with a quarter wave plate, the final intensity of the transmitted light will be

(a)   larger by a factor of 2.
(b)   smaller by a factor of 1/2.
(c)   larger by a factor of 1/cos230°.
(d)   smaller by a factor of cos230°.
(e)   the same as in the original situation.

### QUESTION 4**

Polarized light at 45° to the vertical axis is incident on a quarter wave plate as shown below. The light emerging past the quarter wave plate is

(a)   right circularly polarized.
(b)   left circularly polarized.

### QUESTION 5**

Two parallel laser beams are initially directed from air, into a solid rectangular plastic "cube" having index of refraction n = 1.5, and back into the air. Which diagram below is the most likely path of the two beams?

(a)
(b)
(c)

### QUESTION 6*

This question and the next one refer to this situation:

A laser sends a beam of light from water toward a plastic slab at the surface of the water. Above the plastic slab there is air.

What is the maximum value of the angle θ that the laser beam can make with the vertical and still have the beam of light emerge into the air above the plastic?

(a)   41.81°
(b)   48.75°
(c)   60.07°

### QUESTION 7*

Assume the light beam is shone so that θ = 38°. If the plastic slab is 10 cm thick in the vertical direction, how long did it take the beam to travel through the plastic?

(a)   2.73 × 10-10 s
(b)   3.27 × 10-10 s
(c)   4.49 × 10-10 s
(d)   4.73 × 10-10 s
(e)   5.97 × 10-10 s

### QUESTION 8***

A circuit consists of a capacitor and an inductor. The resistance in the circuit is small and can be neglected. Initially, at t = 0 s, the voltage across the capacitor is at its maximum of VC = 10 V, the charge stored in the capacitor is 1 mC. It is observed that the capacitor discharges to QC = 0 C after t = 0.25 ms. What is the inductance L of the inductor in the circuit?

(a)   63.3 μH
(b)   126.7 μH
(c)   190.0 μH
(d)   253.3 μH
(e)   316.6 μH

### QUESTION 9**

This question and the next one refer to this situation:

A typical electric guitar pickup consists of a coil of several thousand turns of very thin, enamel-coated copper wire wound around a fiber bobbin holding 6 rod-shaped permanent magnets. The figure below shows the 3 (neck, middle, bridge) pickups from a vintage 1959 Fender 'Stratocaster' guitar. A simplified model of an electric guitar pickup is the so-called RLC 'tank' circuit - as shown in the circuit diagram below on the right. The '59 Strat pickup coil has an inductance L = 2.6 H, in series with a resistance R = 5.5 KΩ, and a small capacitance C = 10-10 F in parallel with L and R, as shown. The electric guitar pickups are mounted in proximity to the 6 strings of the electric guitar, magnetizing them. When a magnetized guitar string vibrates, the magnetic flux Φm in the pickup coil varies in time with the string vibrations, inducing a small EMF, V(t), in the electric guitar pickup, which is then amplified in a guitar amplifier to produce an audible sound at the frequency of vibration of the guitar string!

The impedances, Z(ω), of the electric guitar pickup at ω = 0 and at ω = ∞ are:

(a)   Z(ω=0) = 0 ohms and Z(ω=) = 0 ohms
(b)   Z(ω=0) = 0 ohms and Z(ω=) = R ohms
(c)   Z(ω=0) = R ohms and Z(ω=) = 0 ohms

### QUESTION 10**

In the limit R → 0, which of the following frequencies is closest to resonance for the electric guitar pickup?

(a)   fo = 9.9 × 103 Hz
(b)   fo = 6.2 × 104 Hz
(c)   fo = 7.1 × 104 Hz

### QUESTION 11*

This question and the next two refer to this situation:

A series RLC circuit is shown in the figure on the right The resistance R = 200 Ω, inductance L = 2 H and capacitance C = 2 μF.

The instantaneous voltage, V(t), of the sine-wave generator and instantaneous current, I(t), flowing through the RLC circuit are 90° out of phase with each other at the resonant frequency, fo, of the series RLC circuit.

(T)   True
(F)   False

### QUESTION 12*

For this question and the next assume that at the resonant frequency fo of the series RLC circuit, the amplitude of the current is I = 1.0 A.

The voltage amplitude VC across the capacitor at the resonant frequency, fo, of the series RLC circuit is:

(a)   100 V
(b)   500 V
(c)   1000 V

### QUESTION 13***

The RMS energy stored in the capacitor at the resonant frequency fo of this series RLC circuit is:

(a)   0.0 J
(b)   0.35 J
(c)   0.50 J
(d)   0.71 J
(e)   1.00 J

### QUESTION 14***

This and the next question refer to this situation:

A sinusoidally-varying voltage V(t) = Vosinωt with amplitude Vo = 10 V and frequency of f = ω/(2π) = 100 Hz is impressed across the plates of a circular-shaped parallel plate air-gap capacitor of radius a = 1.0 cm and plate separation d= 0.01 mm. The amplitude of Maxwell's displacement current ID flowing across the gap between the plates of this capacitor is:

(a)   0.28 × 10-6 A
(b)   1.75 × 10-6 A
(c)   3.50 × 10-6 A
(d)   6.30 × 10-6 A
(e)   9.45 × 10-6 A

### QUESTION 15***

If the frequency of the voltage signal impressed on the parallel plate capacitor is doubled from f to 2f, the amplitude of the magnetic field Bo at r = a at the mid-plane of the gap between the plates of this capacitor will

(a)   decrease by a factor of four.
(b)   decrease by a factor of two.
(c)   remain the same.
(d)   increase by a factor of two.
(e)   increase by a factor of four.

### QUESTION 16*

This and the next two questions concern the following situation:

A plane electromagnetic wave is propagating in free space. The instantaneous electric field vector is given by E(r,t) = Eocos(kz+ωt)x. The electric field amplitude associated with this plane wave is Eo = 100 V/m.

The corresponding instantaneous magnetic field vector is given by:

(a)   B(r,t) = Bocos(kz+ωt) x
(b)   B(r,t) = -Bosin(kz+ωt) x
(c)   B(r,t) = -Bocos(kz+ωt) y
(d)   B(r,t) = Bosin(kz+ωt) y
(e)   B(r,t) = -Bosin(kz+ωt) z

### QUESTION 17*

The magnetic field amplitude Bo associated with this plane wave is:

(a)   8.85 × 10-12 T
(b)   3.33 × 10-7 T
(c)   100 T

### QUESTION 18*

The magnitude of the intensity Io of the plane electromagnetic wave is:

(a)   6.6 watts/m2
(b)   13.3 watts/m2
(c)   26.6 watts/m2

### QUESTION 19***

Two solenoids have the same number of turns per unit length. Solenoid B is twice as long as solenoid A. The cross sectional area of solenoid B is twice that of solenoid A. The current through both solenoids is I. What is the relationship between the energy stored in the two solenoids?

(a)   UA = ¼ UB
(b)   UA = ½ UB
(c)   UA = UB
(d)   UA = 2 UB
(e)   UA = 4 UB

### QUESTION 20*

This and the next question concern the following situation:

In the circuit below, V = 6 volts, R = 10 ohms, L = 100 mH. The switch has been open for a long time. Then, at time t = 0, the switch is closed.

What is the current I through L for t → ∞ ?

(a)   0.0 A
(b)   0.3 A
(c)   0.6 A

### QUESTION 21***

What is the time constant for the current through the inductor?

(a)   R / L
(b)   R / (2L)
(c)   L / R
(d)   2L / R
(e)   L / (2R)

### QUESTION 22*

This and the next question refer to the following RLC circuit:

Calculate the impedance, Z, of the circuit.

(a)   7.48 Ω
(b)   10.14 Ω
(c)   15.24 Ω
(d)   22.42 Ω
(e)   32.24 Ω

### QUESTION 23*

What is the phase relationship between the voltage of the AC generator, VAC, and the voltage across the resistor, VR?

(a)   VAC and VR are in phase.
(c)   VAC lags VR.

### QUESTION 24*

As shown in the figure below, an ideal iron-core transformer has a primary winding that has N1 = 100 turns of wire and a secondary winding that has N2 = 4000 turns of wire. An RMS AC voltage ε = 25.0 V and RMS current of Ip = 4.0 A excites the primary winding of the ideal transformer at a frequency f = 1000 Hz. A resistor load R = 10 KΩ is connected across the secondary winding of the transformer. The RMS current Is flowing through the resistor load R is:

(a)   0.005 A
(b)   0.100 A
(c)   0.500 A
(d)   1.000 A
(e)   4.000 A

### QUESTION 25***

A series LRC circuit is driven by an AC generator of angular frequency ω = 1000 rad/s. The phasor diagram at time t0 looks as shown below. What is the correct relation between the voltages in the circuit at a later time, t1, with t1 - t0 = 3.142 × 10-3 s? (Note that the voltages VC, VR, and VC used below are signed numbers.)

(a)   VC(t1)  >  VR(t1)  >  VL(t1)
(b)   VC(t1)  >  VL(t1)  >  VR(t1)
(c)   VR(t1)  >  VC(t1)  >  VL(t1)
(d)   VR(t1)  >  VL(t1)  >  VC(t1)
(e)   Cannot be determined from the information given.

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.