### Spring 2005 Physics 102 Hour Exam 2(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 101. The exam period was 90 minutes; the mean score was 69.6; the median was 75. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1**

This and the next question pertain to the following situation.

A 30-cm-long conducting rod (rod A) with mass 10 g is suspended by conducting wires of negligible mass as shown in the figure. The rod is 10 cm above the surface of a table. On the table, there is another long rod (rod B) parallel to rod A. Rod B is carrying a current of 200 A.

What is the minimum current in rod A necessary to support the weight of the rod so that there is no tension in the wires?

(a)   51 A
(b)   102 A
(c)   204 A
(d)   408 A
(e)   817 A

### QUESTION 2*

The direction of current in rod A necessary to support the weight of the rod must be in the opposite direction as in rod B.

(T)   True
(F)   False

### QUESTION 3*

This and the next three questions pertain to the following situation.

Two particles, A (mA=1.7 × 10-27 kg , QA= 1.6 × 10-19 C ) and B (mB= 3.4 × 10-27 kg , QB= -3.2 × 10-19 C ) enter a box with uniform magnetic field B=7.5 T. Particle A enters with velocity vA=106 m/s and follows trajectory A.

What is the direction of the magnetic field inside the box?

(a)   into the page
(b)   out of the page
(c)   up
(d)   down
(e)   right

### QUESTION 4*

The speed of particle A remains the same along trajectory A.

(T)   True
(F)   False

### QUESTION 5*

The distance L, from entry to the point where trajectory A exits the spectrometer (which equals the diameter of the semicircle) is

(a)   L = 2.84 × 10-3 m
(b)   L = 3.75 × 10-3 m
(c)   L = 4.25 × 10-3 m

### QUESTION 6*

Particle B also enters with velocity vB = 106 m/s. Which trajectory in the figure below will it follow?

(a)   trajectory 1
(b)   trajectory 2
(c)   trajectory 3

### QUESTION 7*

This and the next two questions pertain to the following situation.

A U-shaped conducting rod is connected to two conducting wires at points A and B as shown in the figure below. The rod is allowed to rotate about an axis connecting the pivot points A and B. A current of 3.5 A passes through the wires and the rod (as indicated by short arrows). A uniform B field of 0.04 T is applied along a direction at 45° angle with the sides of the rod. The length of each segment of the rod is 50 cm.

What is the magnitude of the magnetic force on left side (segment AD) of the rod?

(a)   0 N
(b)   0.0700N
(c)   0.0495N
(d)   0.0350N
(e)   0.0990N

### QUESTION 8*

The directions of the forces on the left side (segment AD) and right side (segment BC) of the rod are

(a)   left: out of the page, right: into the page
(b)   left: into the page, right: out of the page
(c)   left: out of the page, right: out of the page

### QUESTION 9**

The magnitude of the torque due to the force acting on the bottom side (segment DC) of the rod is

(a)   0 Nm
(b)   0.0495 Nm
(c)   0.0247 Nm

### QUESTION 10**

This and the next two questions pertain to the following situation.

A rectangular wire loop is carried in the y-direction at a constant speed of 10 m/s. The loop has a total loop resistance of 10 Ω and is lying in the x-y plane. It is 30 cm long and 10 cm wide. A region of constant and uniform magnetic field of magnitude 10 T pointing in the positive z-direction extends from y = 0 to y = 60 cm as indicated in the figure. At time t = 0 the leading edge of the loop enters the magnetic field region.

From t = 0 to t = 0.03 sec a counter clockwise current flows in the circuit.

(T)   True
(F)   False

### QUESTION 11**

What is the mechanical power that must be supplied to move the loop during the time interval 0 < t < 0.03 sec?

(a)   5.0 W
(b)   10.0 W
(c)   20.0 W
(d)   40.0 W
(e)   100.0 W

### QUESTION 12**

Between t = 0.06 and 0.09 sec the loop leaves the field region. Which one of the following statements is true?

(a)   A negative amount of work is done pulling the loop out of the field region during this time interval.
(b)   The same amount of work is done pulling the loop out of the field region as pulling it into the field region.
(c)   Less work would be done if the loop were pulled through at a faster speed.

### QUESTION 13***

This and the next two questions pertain to the following situation.

A coil consisting of two square loops, connected in series, rotates at f = 60 revolutions per second, that is ω = 2π radians/sec. It does so around the y-axis and through a magnetic field of 1 Tesla pointing in the positive z-direction. A snapshot of the rotating coil at time t=0 is shown in the figure. At time t=0 the plane of the coil is in the x-y plane. The loops are 10 cm by 10 cm in dimension and have no resistance of their own. A 1 Ω resistor is connected across the coils as shown.

At time t = 0 (shown in the figure)

(a)   the current in the loops is flowing clockwise.
(b)   the current in the loop is flowing counter clockwise.
(c)   the current is zero.

### QUESTION 14**

The maximum value of the current flowing in the loop is

(a)   1.20 amp
(b)   3.77 amp
(c)   7.54 amp
(d)   56.85 amp
(e)   113.70 amp

### QUESTION 15**

If the magnetic field were doubled, the power dissipated in the resistor would double.

(T)   True
(F)   False

### QUESTION 16**

This and the next question pertain to the following situation.

An ideal transformer with 5 turns on the primary and 10 turns on the secondary is shown in the figure. A sinusoidal voltage source having V(t) = 10 sin(100t) volts is connected across the primary and a 1 Ω resistor is connected across the secondary.

The current in the secondary oscillates at 200 rad/sec.

(T)   True
(F)   False

### QUESTION 17***

What is the maximum value of the current in the primary circuit (not the secondary)?

(a)   2.0 amp
(b)   5.0 amp
(c)   10.0 amp
(d)   20.0 amp
(e)   40.0 amp

### QUESTION 18***

This and the next two questions pertain to the following situation.

A uniform magnetic field is pointed in the z-direction and has a time dependence as shown in the figure. It is zero at t = 0 as well as at t = 24 sec. Between 10 and 18 sec it is 1 T, and for t > 30 sec it is -1 T. A square conducting coil of length 10 cm on a side lies in the x-y plane. The resistance of the coil is 10 Ω.

At t = 24 sec which statement is true?

(a)   No current flows in the loop.
(b)   A counter-clockwise current flows in the loop.
(c)   A clockwise current flows in the loop.

### QUESTION 19**

The magnitude of the current at 5 seconds is

(a)   10.0 μA
(b)   3.14 μA
(c)   33.3 μA
(d)   50.0 μA
(e)   100.0 μA

### QUESTION 20**

The EMF is zero at 32 seconds.

(T)   True
(F)   False

### QUESTION 21*

The voltage VR across a resistor in the following AC circuit is shown in the graph below. What is the RMS voltage across the resistor?

(a)   14.14 V
(b)   20.00 V
(c)   40.00 V

### QUESTION 22**

In a complex circuit, the current IL flowing through an inductor is found to vary with time as shown in the graph at right.

Which of the graphs below best illustrates the energy UL in the inductor as a function of time?

(a)
(b)
(c)

### QUESTION 23*

Voltage phasor diagrams for the circuit at right are shown below. Each diagram corresponds to a different time.

In which one of the phasor diagrams is the voltage across the resistor greatest?

(a)
(b)
(c)

### QUESTION 24**

In the circuit shown below, a "signal generator" drives current through a resistor, capacitor, and inductor so that the voltage across the resistor, VR, is as shown in the graph. Recall that the current in this series circuit is proportional to the voltage across the resistor.

Which one of the following graphs best illustrates the voltage across the inductor as a function of time?

(a)
(b)
(c)

### QUESTION 25*

Two inductors are shown in the figure below. Both inductors are wound to have the same diameter and the same number of turns per meter, but one is 10 cm long, while the other is 20 cm long.

The ratio of the inductances for the 20 cm and 10 cm inductors L20 / L10 is 4 / 1 .

(T)   True
(F)   False

### QUESTION 26*

An AC circuit is shown in the figure below.

When the generator frequency f is tuned so that the capacitive and inductive reactances are equal, what is the maximum current I flowing in the circuit?

(a)   I = 1.00 × 10-7 A
(b)   I = 6.28 × 10-3 A
(c)   I = 1.01 × 10-2 A
(d)   I = 1.00 × 10-1 A
(e)   I = 3.14 × 10-2 A

### QUESTION 27*

An AC circuit is shown in the figure below.

The generator frequency f is set to 7000 Hz. What is the magnitude of the phase difference (in degrees) between the current in the circuit and the generator's voltage?

(a)   Φ = 0.238°
(b)   Φ = 11.99°
(c)   Φ = 102.23°
(d)   Φ = 121.25°
(e)   Φ = 166.72°

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.