### Fall 2006 Physics 102 Hour Exam 2(28 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 112. The exam period was 90 minutes; the mean score was 83.8; the median was 86. Click here to see page1 page2 of the formula sheet that came with the exam.

• A physics 102 light bulb acts just like a resistor: its resistance is constant, independent of the current flowing through the light bulb. The bulb's brightness increases with increasing current.
• A reminder about prefixes: p (pico) = 10-12; n (nano) = 10-9; μ (micro) = 10-6; m (milli) = 10-3; k (kilo) = 10+3; M or Meg (mega) = 10+6; G or Gig (giga) = 10+9.

### QUESTION 1**

This and the next question pertain to the following situation.

A pair of conducting rails is connected to a resistor and a 5 V battery as shown in the following figure. A movable conducting bar is placed in contact with the rails. Initially the position of the conducting bar is held fixed. The entire device lies in a plane perpendicular to a magnetic field of strength 0.5 T.

The conducting bar is now moved slowly to the right. Relative to the current that had been flowing through the resistor while the bar was stationary, the current I

(a)   increases.
(b)   decreases.

### QUESTION 2**

The conducting bar is now moved rapidly with speed v in the direction that reduces the current so that I becomes exactly zero. The speed v is:

(a)   0.625 m/s
(b)   2.5 m/s
(c)   12.5 m/s
(d)   40 m/s
(e)   62.5 m/s

### QUESTION 3**

This and the next question pertain to the following situation.

A conducting metal band containing a 5 Ω resistor is formed into a circle of radius R = 2 m as shown in the diagram. The band passes through a current sensor that also controls the strength of an adjustable, externally created magnetic field. (The electromagnet that creates this uniform field is not shown in the diagram.) The circle always lies in the plane of the paper, perpendicular to the magnetic field.

The current sensor/magnet power supply is programmed to adjust the external magnetic field so that a constant current of 0.1 A flows around the loop. At time t = 0 the magnetic field happens to have the value B = 0. What is the value of B at t = 1 second?

(a)   B = 0.040 T
(b)   B = 0.100 T
(c)   B = 0.314 T
(d)   B = 1.687 T
(e)   B = 2.000 T

### QUESTION 4**

If the radius of the loop were halved so that R = 1 m, how would the rate of change of the magnet field, ΔBt, need to change in order to maintain a 0.1 A current in the loop?

(a)   ΔBt would need to increase by a factor of 2.
(b)   ΔBt would need to increase by a factor of 4.
(c)   ΔBt would need to decrease by a factor of 2.
(d)   ΔBt would need to decrease by a factor of 4.
(e)   ΔBt would not need to change.

### QUESTION 5*

This and the next question pertain to the following situation.

A rectangular loop (made from a single turn of wire) has sides a = 0.2 m and b = 0.1 m. The coil rotates about the y axis with angular velocity Ω = 20 rad/s in a uniform magnetic field B = 0.05 T that is parallel to the x axis. A light bulb with resistance 12 Ω is connected in series with the loop as shown in the diagram.

What is the maximum current that flows through the light bulb?

(a)   65.8 mA
(b)   12.2 mA
(c)   1.67 mA

### QUESTION 6**

The bulb's brightness varies periodically as the loop rotates. At the instant shown in the diagram, when the plane of the loop is perpendicular to the magnetic field, the bulb is dimmest.

(T)   True
(F)   False

### QUESTION 7*

A laboratory power source supplies a voltage V(t) = 480sin(320t) volts to an experiment. What is the frequency f in Hz (cycles per second) provided by this power source?

(a)   320 Hz
(b)   2010 Hz
(c)   50.9 Hz

### QUESTION 8*

A transformer with a 100-turn primary coil and 300-turn secondary coil is wired to an AC signal generator and a resistor with R = 50 Ω as shown in the following diagram.

The peak power delivered to the resistor attached to the transformer's secondary is 75 W. What is the signal generator's peak voltage?

(a)   1.5 V
(b)   5.0 V
(c)   20.4 V
(d)   3750 V
(e)   36000 V

### QUESTION 9*

It might be necessary to enclose the International Linear Collider's positron damping ring vacuum pipe in a long solenoid to suppress instabilities. Imagine that the required solenoid is 6,200 m long with diameter 0.1 m, and is wound with 100 turns per meter.

What is the inductance of this solenoid?

(a)   0.612 H
(b)   62000 H
(c)   1.344 mH

### QUESTION 10*

The diagram illustrates a series LRC circuit driven by a sine wave generator and an oscilloscope display that indicates the voltages VL and VC across the inductor and capacitor respectively. Note that the maximum value of VL is greater than the maximum value of VC.

In order to make the maximum value of VL become less than the maximum value of VC one could

(a)   increase the maximum voltage of the sine wave generator.
(b)   decrease the frequency of the sine wave generator.
(c)   increase the value of R used in the circuit.

### QUESTION 11*

This and the next question pertain to the following situation.

In the circuit shown the switch S is initially open and the two capacitors are fully discharged.

At time t = 0 the switch S is closed. What is the current through the resistor R immediately after S is closed?

(a)   10000 A
(b)   2.5 mA
(c)   0.0025 mA
(d)   2.5 A
(e)   10 mA

### QUESTION 12**

What is the ratio of the currents at t = 25 msec and t = 0? (Recall that 25 msec is 2.5 × 10-2 sec.)

(a)   I(25 msec) / I(0) = 0.361
(b)   I(25 msec) / I(0) = 0.010
(c)   I(25 msec) / I(0) = 0.650
(d)   I(25 msec) / I(0) = 0.249
(e)   I(25 msec) / I(0) = 0.189

### QUESTION 13***

This and the next question pertain to the following situation.

In the circuit shown the switch S1 is initially open and the capacitor C is fully discharged.

Switch S1 is now closed. Which one of the following represents the correct time-dependence of the current through resistor R1?

(a)
(b)
(c)

### QUESTION 14**

After a long time S1 is opened again and the capacitor is allowed to discharge. What is the time constant, τ, for the decrease in the capacitor's voltage?

(a)   1.5 ms
(b)   6 ms
(c)   45 ms
(d)   18 μs
(e)   2.2 s

### QUESTION 15**

This and the next question pertain to the following situation.

A charged particle, q, is moving in a uniform magnetic field and travels in a circle of radius R, as shown.

What is the sign of q?

(a)   positive
(b)   negative

### QUESTION 16*

What is the mass of q?

(a)   2.26 ×10-11 kg
(b)   3.02 ×10-13 kg
(c)   2.46 × 10-12 kg

### QUESTION 17*

This and the next question pertain to the following situation.

A proton with charge q = +1.6 × 10-19 C and mass m = 1.67 × 10-27 kg is initially traveling horizontally in a magnetic field with velocity v = 800 m/s, as shown below. The proton experiences a downward acceleration due to gravity of g = 9.8 m/s2. If the magnetic field were zero, the proton would follow the downward, parabolic trajectory shown in the dashed line.

How large a magnetic field would have to be applied to force the proton to move in a straight line?

(a)   5 × 10-8 T
(b)   4.44 ×10-12 T
(c)   1.5 T
(d)   1.28 ×10-10 T
(e)   23 mT

### QUESTION 18**

Which way would the field have to point?

(a)
(b)

### QUESTION 19*

An aluminum wire with mass/unit length of ρ = 2.7 ×10-4 kg/m lies on the ground, running east - west. The wire feels the earth's magnetic field, which has magnitude B = 5 × 10-5 T. Assume the wire is in Panama, where the Earth's magnetic field runs due north, i.e. parallel to the ground. A current flows in the wire west-to-east as shown.

How large would the current have to be to lift the cable off the ground? Recall, g = 9.8 m/s2.

(a)   2.2 × 106 A
(b)   18600 A
(c)   5325 A
(d)   340 A
(e)   52.9 A

### QUESTION 20*

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

In an RLC circuit, the following three elements are connected in series: a 10 mH inductor L, a 20 Ω resistor R, and a 120 μF capacitor C. The AC generator has a peak voltage of 1V, and a frequency of 50 Hz. Assume the resistance of the inductor is zero.

Across which of the following elements of the circuit is the maximum voltage drop the greatest?

(a)   L
(b)   R
(c)   C

### QUESTION 21**

The following drawing indicates the voltage across the circuit elements as a function of time. The voltage drop across the resistor is labeled A (solid line). The voltage drops across which elements are shown by the dashed and dotted lines?

(a)   C = generator; B = capacitor
(b)   C = inductor; B = capacitor
(c)   C = inductor; B = generator

### QUESTION 22*

The current through the circuit is in phase with the voltage drop across which element?

(a)   L
(b)   R
(c)   C

### QUESTION 23*

What is the maximum current in the circuit?

(a)   1.29 A
(b)   0.39 A
(c)   32.5 mA
(d)   92.8 mA
(e)   0.21 mA

### QUESTION 24*

What is the phase angle between the generator voltage and the current in the circuit?

(a)   0°
(b)   15.23°
(c)   -49.43°
(d)   -76.15°
(e)   100. 3°

### QUESTION 25**

Which one of the following is correct?

(a)   The current leads the generator voltage.
(b)   The generator voltage leads the current.

### QUESTION 26*

Removing which of the following elements would reduce the power consumed by the circuit?

(a)   R
(b)   L
(c)   C

### QUESTION 27*

What is the resonance frequency of the circuit?

(a)   42.0 Hz
(b)   145 Hz
(c)   2.34 kHz

### QUESTION 28**

If the frequency of the AC generator is adjusted closer to the resonance frequency, the average power dissipated in the circuit would

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

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.