### Fall 2010 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 123. The exam period was 90 minutes; the average score was 89.0; the median score was 90. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

This and the next four questions concern the following situation:

A series RLC circuit with L = 25 mH, C = 0.8 μF and R = 7 Ω is driven by a generator with a maximum emf of 12 V and a variable angular frequency ω.

Find Imax at resonance.

(a)   Imax = 0 A
(b)   Imax = 1.7 A
(c)   Imax = 3.8 A
(d)   Imax = 4.3 A
(e)   Imax = 6.9 A

### QUESTION 2*

At resonance, the current

(a)   leads the generator voltage by 90°.
(b)   lags the generator voltage by 90°.
(c)   is in phase with the generator voltage.

### QUESTION 3**

If the inductance L is doubled (keeping all other quantities given, including the generator frequency, the same), compared to the power dissipated when the circuit was at resonance, the power now dissipated in the resistor will

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

### QUESTION 4*

At ω = 8000 rad/sec the impedance Z of the circuit is:

(a)   Z = 7 Ω
(b)   Z = 12.3 Ω
(c)   Z = 27.1 Ω
(d)   Z = 44.3 Ω
(e)   Z = 172 Ω

### QUESTION 5*

At ω = 8000 rad/sec the phase angle between the generator voltage and the current through the resistor is

(a)   11.3°.
(b)   23.4°.
(c)   80.9°.
(d)   90°.
(e)   not enough information to determine

### QUESTION 6*

Consider a spherical rain drop in the air. A laser beam is directed at the rain drop from the left and slightly above the central axis (see figures). Which of the following diagrams best indicates the trajectory of the light? (Note, the dotted lines cross in the center of each rain drop, and therefore indicate the normal to the surface.)

(a)
(b)
(c)

### QUESTION 7***

This question and the next one concern the following situation:

The current in a series RLC circuit leads the generator voltage by φ = 30°. The circuit, containing an inductor L = 400 mH and a resistor R = 50 Ω, is driven by a generator operating at ω = 100 rad/s with a maximum emf of 10 V. The capacitance is unknown.

The value of the capacitance C is

(a)   C = 32 μF.
(b)   C = 145 μF.
(c)   C = 580 μF.
(d)   C = 900 μF.
(e)   C = 1.18 mF.

### QUESTION 8***

In terms of the maximum energy UC,max stored in the capacitor and the angle φ by which the current leads the generator voltage, the energy UC stored in the capacitor when the time is t = π/2ω is:

(a)   UC = UC,max sin2φ
(b)   UC = UC,max sinφ
(c)   UC = UC,max tan2φ
(d)   UC = UC,max tanφ
(e)   UC = UC,max cos2φ

### QUESTION 9**

This question and the next two refer to this situation:

The plot below depicts the electric field component of a linearly polarized, electromagnetic plane wave traveling through vacuum. E(r,t) propagates in the negative z-direction and toward an observer located at z = 0. (Note that x is directed into the page.)

The magnetic field associated with this wave may have the form (assuming k and ω have their usual definitions):

(a)   B(r,t) = xBmaxsin(kz-ωt)
(b)   B(r,t) = xBmaxsin(kz+ωt)
(c)   B(r,t) = zBmaxsin(kz-ωt)
(d)   B(r,t) = -xBmaxsin(kz+ωt)
(e)   B(r,t) = -xBmaxsin(kz-ωt)

### QUESTION 10**

At time t = 3π/2ω, the observer measures the magnitude of the Poynting vector to be |S| = 0.063 W/m2. What is the maximum electric field Emax of the electromagnetic wave? (Assume the magnetic field takes one of the forms above.)

(a)   Emax = 0.51 V/m
(b)   Emax = 0.89 V/m
(c)   Emax = 4.9 V/m
(d)   Emax = 8.3 V/m
(e)   Emax = 15.5 V/m

### QUESTION 11***

If the observer begins moving in the positive z-direction, the speed of propagation of the wave will

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

### QUESTION 12**

A galaxy is receding from us at a speed v = 0.96c. Light emitted by the galaxy at a wavelength of 450 nm would appear to us to have a wavelength λearth of:

(a)   λearth = 64 nm
(b)   λearth = 445 nm
(c)   λearth = 450 nm
(d)   λearth = 455 nm
(e)   λearth = 3150 nm

### QUESTION 13*

An ideal transformer has 75 turns in the primary coil and N turns in the secondary coil. A 120 V rms 60Hz AC voltage source is connected to the primary coil. A 10 Ω resistor is connected to the secondary coil, forming a secondary circuit. The average power dissipated in the secondary circuit is 160 W. What is the number Ns of turns in the secondary coil?

(a)   Ns = 25
(b)   Ns = 75
(c)   Ns = 400

### QUESTION 14*

This and the next question concern the following situation:

As shown at right below, a laser is directed into a water tank (filled with water having an index of refraction n2 at the laser wavelength) at an angle θ1 from the vertical and strikes the bottom of the tank at point A, a horizontal distance r away from B, the spot directly underneath the place where the light enters the water.

The distance r is:

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

### QUESTION 15*

The index of refraction of water for red light is 1.331, while the index of refraction of water for green light is 1.336 . The angle of refraction θ2 would be

(a)   the same for a green and a red laser.
(b)   smaller for a red laser than for a green laser.
(c)   smaller for a green laser than for a red laser.

### QUESTION 16*

Consider the following arrangement of 9 polarizers; the first has a transmission axis oriented at 10° with respect to the horizontal, the second at 20°, … and the 9th at 90° (i.e., vertical). The incident light is horizontally polarized.

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

(a)   If / Ii = 0
(b)   If / Ii = 2.1 × 10-14
(c)   If / Ii = 0.53
(d)   If / Ii = 0.76
(e)   If / Ii = 1

### QUESTION 17*

Now consider three possible incident polarizations: besides horizontal (H), consider circularly polarized (C), and vertically polarized (V). Which of the following would describe the relationship among the transmitted intensities?

(a)   IH > IC > IV
(b)   IH = IC > IV
(c)   IH = IC = IV
(d)   IH < IV < IC
(e)   IH < IC < IV

### QUESTION 18*

The transmitted light beam (after the final polarizer) will

(a)   have a vertical polarization direction.
(b)   have a polarization dependent on the direction of the incident polarization direction.
(c)   be unpolarized.

### QUESTION 19*

This and the next question concern the following situation:

The switch has been in position a for a long time, completely charging the capacitor. At t = 0 the switch is thrown to position b. The values of the battery voltage, V, and the capacitance, C are given; the maximum current Imax is measured after the switch is thrown to position b.

Find the inductance L.

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

### QUESTION 20***

Find the earliest time t1, after t = 0, that the energy stored in the capacitor is equal to the energy stored in the inductor. It might help to sketch the current as a function of time.

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

### QUESTION 21*

This question and the next two concern the following situation:

An object (bold arrow) is located at a distance of 3f / 2 (i.e. at x = -3f / 2) in front of a diverging lens as shown in the figure. Note that f is positive, so the focal length of this lens is -f.

What is the location xi of the image?

(a)   xi = -3f / 5
(b)   xi = -3f / 2
(c)   xi = 3f / 2
(d)   xi = f / 2
(e)   xi = f / 5

### QUESTION 22**

Choose the correct description of the image in the situation above.

(a)   The image is real and inverted.
(b)   The image is virtual and inverted.
(c)   The image is real and upright.
(d)   The image is virtual and upright.
(e)   There is no image formed.

### QUESTION 23**

Suppose the object is now placed at x = -f. What is the magnification M?

(a)   M = 0
(b)   M = 1/2
(c)   M = 1

### QUESTION 24***

This question and the next one concern the following situation:

A constant current I is supplied for a brief time to charge a parallel plate capacitor. The capacitor has circular plates of radius R with a gap d (d << R). Point 1 is at a distance R + d from the wire, and point 2 is at a distance R + d from the center of the capacitor.

During the time interval that the constant current I is flowing through the capacitor, the magnetic field at point 2, B2 is:

(a)   B2 > B1
(b)   B2 = B1
(c)   0 < B2 < B1
(d)   B2 = 0
(e)   not enough information to tell

### QUESTION 25**

After the capacitor is charged and the current I goes to zero

(a)   the electric flux and the magnetic field between the plates are both zero.
(b)   the electric flux between the plates is zero and the magnetic field between the plates is non-zero.
(c)   the electric flux between the plates is non-zero and the magnetic field between the plates is zero.

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.