### Spring 2010 Physics 212 Hour Exam 3(24 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 100. The exam period was 90 minutes; the average score was 76.4; the median score was 78. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

This and the next three questions concern the following situation:

A circuit made with a battery, a switch, an inductor. and three resistors is shown in the figure. To begin with, switch S has been open for a long time. Then at time t = 0 the switch is closed.

The initial current through the inductor immediately after the switch is closed is 0 A.

(T)   True
(F)   False

### QUESTION 2**

What is the inductance L of the inductor if immediately after the switch is closed the magnitude of the time derivative of the current is:    | dI / dt | = 4.15 × 103  ?

(a)   L = 0.19 mH
(b)   L = 0.56 mH
(c)   L = 0.96 mH
(d)   L = 1.93 mH
(e)   L = 2.89 mH

### QUESTION 3*

After being closed for a long time, the switch S is now opened.

What is the direction of the current in the right hand loop containing L, R2 and R3 immediately after the switch is opened?

(a)   clockwise
(b)   counterclockwise

### QUESTION 4*

What is the time constant τ for the circuit after the switch is opened?

(a)   τ = L / R1
(b)   τ = L / (R1+R2)
(c)   τ = L / (R1+R2+R3)

### QUESTION 5**

This and the next two questions concern the following situation:

A circuit made up of a battery, a switch, an inductor, a capacitor and a resistor is shown in the figure below. After being closed for a long time, the switch S is opened at time t = 0.

Immediately after the switch is opened, what is the direction of the current through the capacitor?

(a)   toward the top of the page
(b)   toward the bottom of the page
(c)   the current is 0

### QUESTION 6**

What is the voltage VC across the capacitor when the charge on the capacitor is half of its maximum value?

(a)   1.34 volts
(b)   1.90 volts
(c)   2.68 volts
(d)   4.02 volts
(e)   7.20 volts

### QUESTION 7**

How long would you have to wait after opening the switch to measure a 0 current through the inductor?

(a)   The current is initially 0 through the inductor so you don't have to wait at all.
(b)   7.0 × 10-4 s
(c)   1.4 × 10-3 s
(d)   2.1 × 10-3 s
(e)   2.8 × 10-3 s

### QUESTION 8*

This question and the next one concern the following situation:

A circular capacitor is hooked up to some external electronics that cause a constant current I to flow into it for a brief period of time. This problem studies what happens in the vicinity of the capacitor during that time period. The figures below shows a perspective and a side view of the capacitor and the wires coming in and out of it. The radius of the capacitor is R, the gap between the plates is d and R >> d. This means you can assume that the electric field in the capacitor is uniform and directed straight across the gap, although it may change with time. Three points, labeled 1, 2 and 3, are located a distance R/2 from the center line, with points 1 and 3 outside and point 2 inside the capacitor.

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

(a)   directed out of the page.
(b)   directed into the page.

### QUESTION 9**

Compare the magnitude of the magnetic field at points 1, 2 and 3 during this time interval. When computing magnetic fields, you may treat all wires as being infinitely long. This means that when calculating the magnetic field at points 1 and 3 you may use the corresponding formula that gives the magnetic field from an infinitely long wire.

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

### QUESTION 10*

This question and the next two refer to this situation:

A monochromatic laser beam is polarized in the x- direction and propagates in the positive z-direction along the z-axis as shown in the figure. It passes through an ideal quarter wave plate at the origin. The fast and slow axes are oriented at 45° relative to the x-axis. Then, at z = d the light beam passes through an ideal linear polarizer with the polarization direction tilted at 45° relative to the x-axis as shown in the figure.

The intensity of the beam after it passes through the quarter wave plate is

(a)   equal to the incident intensity.
(b)   one half the incident intensity.
(c)   one quarter the incident intensity.

### QUESTION 11***

Assume the maximum amplitude of the electric field of the incident beam before passing through the quarter wave plate is E0. After passing through the linear polarizer located at z = d, a possible expression for the electric field of the wave is

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

### QUESTION 12*

If E0 is 1000 V/m and the beam area is 10-6 m2, what is the average power of the incident light beam?

(a)   Pave = 0.33 mW
(b)   Pave = 0.57 mW
(c)   Pave = 0.67 mW
(d)   Pave = 1.33 mW
(e)   Pave = 1.67 mW

### QUESTION 13*

A laser beam is incident from vacuum into a transparent glass slab with an index of refraction of 1.5. Which picture shows the trajectory of the beam as it traverses the slab?

(a)
(b)
(c)

### QUESTION 14*

A glass slab with index of refraction equal to 1.5 is immersed in a liquid having index of refraction equal to 1.2 as shown in the figure. What is the minimum incidence angle in the glass slab at which total internal reflection is observed?

(a)   θ = 27.4°
(b)   θ = 41.8°
(c)   θ = 45.0°
(d)   θ = 53.1°
(e)   θ = 56.4°

### QUESTION 15*

A snapshot of the electric field of a sinusoidal electromagnetic wave, taken at t = 0, is shown in the figure. The wave is polarized in the x-direction and is propagating in the positive z-direction.

Which expression correctly gives the magnetic field of this wave?

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

### QUESTION 16*

An unpolarized light beam propagates through four ideal linear polarizers as shown in the figure below. The first polarizer is oriented vertically. The polarization axes of the following three polarizers are tilted from vertical by the angles given in the figure.

(a)   I4 / I0 = 0.211
(b)   I4 / I0 = 0.326
(c)   I4 / I0 = 0.404
(d)   I4 / I0 = 0.571
(e)   I4 / I0 = 0.653

### QUESTION 17*

This and the next two questions concern the following situation:

A series RLC circuit is driven by a sinusoidal voltage generator. It is shown in the figure below. The resistance is 200 Ω. The maximum voltage amplitude supplied by the voltage generator VG is 141 V. The voltage VR across the resistor is measured to be VR = 100 cos(1000πt) volts. The voltages measured across the resistor and the voltage generator as functions of time are also sketched below. In particular, it is found that the voltage across the generator lags the voltage across the resistor.

The frequency f produced by the generator is:

(a)   500 Hz
(b)   1000 Hz
(c)   1500 Hz
(d)   250 Hz
(e)   100 Hz

### QUESTION 18*

The reactance (X = XL-XC) of the circuit is

(a)   positive.
(b)   negative.
(c)   zero.

### QUESTION 19**

The time-averaged power supplied by the generator is:

(a)   100 W
(b)   70.5 W
(c)   50 W
(d)   35.25 W
(e)   25 W

### QUESTION 20*

This and the next two questions concern the following situation:

A sinusoidal voltage generator drives a series RLC circuit as shown in the figure below.

As ω → 0, the generator voltage leads the current.

(T)   True
(F)   False

### QUESTION 21*

Which one of the following statements is true concerning average power in the RLC circuit?

(a)   The average power supplied by the generator always exceeds Irms2 R .
(b)   The average power supplied by the generator always equals Irms2 R .
(c)   The average power supplied by the generator is always less than Irms2 R .

### QUESTION 22**

If the angular frequency of the generator exceeds 1/sqrt(LC), the average energy stored in the inductor is greater than the average energy stored in the capacitor.

(T)   True
(F)   False

### QUESTION 23*

This question and the next one concern the following situation:

A sinusoidal voltage generator drives a series RL circuit as shown in the figure below. The angular frequency of the generator is ω = 2000 rad/sec. The rms EMF supplied by the generator is 100 V and the rms current in the circuit is measured to be 2 A. The time-averaged power supplied by the generator is 120 W.

The resistance R is

(a)   60 Ω.
(b)   30 Ω.
(c)   120 Ω.

### QUESTION 24*

The EMF supplied by the generator leads the current by

(a)   53°.
(b)   45°.
(c)   37°.

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.