### Fall 2010 Physics 102 Hour Exam 2(26 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 117. The exam period was 90 minutes; the mean score was 95.5; the median was 99. Click here to see page1 page2 page3 of the formula sheet that came with the exam.

• 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*

When a series RLC circuit is driven at a very high frequency by an AC generator, which circuit component(s) can be ignored?

(a)   resistor
(b)   capacitor
(c)   inductor
(d)   capacitor and inductor
(e)   inductor and resistor

### QUESTION 2*

Which of the following two equations is (are) always true for a series RLC circuit?
I)  Vgen(t) = VL(t) + VR(t) + VC(t)
II)  Vgen,max = VL,max + VR,max + VC,max

(a)   I
(b)   II
(c)   I and II

### QUESTION 3*

A transformer for a laptop computer supplies a maximum EMF of 20 V when plugged into an AC power supply of 120 V (maximum voltage). If it has 780 turns in its primary coil, how many turns does the secondary coil have?

(a)   130
(b)   156
(c)   3900
(d)   4680
(e)   none of the above

### QUESTION 4*

This question and the next one pertain to the the following situation.

The phasor diagram for a series RLC circuit is shown here with phasors VR, VL and VC corresponding to the resistor, capacitor, and inductor, respectively. Three additional phasors (A, B, and C, in dotted lines) are included as well.

Which of these three phasors corresponds to that of the generator?

(a)   A
(b)   B
(c)   C

### QUESTION 5*

What conclusion can you draw about the driving frequency?

(a)   The frequency is less than the resonant frequency.
(b)   The frequency is the same as the resonant frequency.
(c)   The frequency is greater than the resonant frequency.

### QUESTION 6**

Three circular wire loops are stacked as shown below with the top and bottom loop initially carrying no current and the central loop carrying a finite counterclockwise current.

If the current in the central loop is increased, in what directions will induced currents in the top loop and the bottom loop flow?

(a)   Top - counterclockwise; Bottom - counterclockwise
(b)   Top - counterclockwise; Bottom - clockwise
(c)   Top - clockwise; Bottom - counterclockwise
(d)   Top - clockwise; Bottom - clockwise
(e)   There are no induced currents.

### QUESTION 7*

Two isotopes of uranium are separated by charging each atom to q = 1.6 × 10-19 C and subjecting them to a 1 T magnetic field. The masses of the isotopes, U-235 and U-238, are M235 = 3.90 × 10-25 kg and M238 = 3.95 × 10-25 kg, respectively. The isotopes follow circular arcs as shown below.

Assuming that all particles have the same speed, what is the ratio R235 / R238 of the radii of the paths taken by the two isotopes?

(a)   0.987
(b)   1.217
(c)   2.090

### QUESTION 8*

You are given a simple circuit consisting of a resistor R = 10 Ω, a capacitor C = 30 μF, an inductor L = 0.04 H and an AC generator. The generator operates at a peak voltage of 15 V and a frequency of 200 Hz.

What is the phase angle φ associated with the generator?

(a)   -12°
(b)   27°
(c)   41°
(d)   67°
(e)   72°

### QUESTION 9*

This question and the next two deal with the situation described below.

A charged particle travels through two chambers as shown below. It enters Chamber 1 from below and exits Chamber 2 from above. The particle moves at a speed of 150 m/s. The magnetic field in Chamber 2 has a magnitude of 0.8 T.

Assuming the particle is negatively charged, what is the direction of the magnetic field in Chamber 1?

(a)   into the page
(b)   out of the page
(c)   to the right

### QUESTION 10**

The particle travels a path of length 2.7 meters through Chamber 2. If it has a mass of 32 grams, what is the magnitude of the charge of the particle?

(a)   2.22 C
(b)   3.49 C
(c)   6.98 C
(d)   2220 C
(e)   3490 C

### QUESTION 11*

Which one of these statements about the magnitudes of the magnetic fields in each chamber B1 and B2 is correct?

(a)   B1 > B2
(b)   B1 = B2
(c)   B1 < B2

### QUESTION 12*

This question and the next two deal with the situation described below.

As shown below, an RLC circuit consists of a resistor R, a variable capacitor C, an inductor L and an AC power source generating a voltage of V(t) = V0 sin(2π f t). Circuit parameters R, L and V0 are fixed at R = 50 Ω, L = 4 mH and V0 = 20 V, and the generator frequency is set to f = 5 kHz.

To what value should you change the capacitance C for the circuit to be in resonance with the frequency f of the generator?

(a)   2.5 × 10-7 F
(b)   7.5 × 10-3 F
(c)   8.3 F

### QUESTION 13*

For this resonant condition, what is the average power dissipated by the circuit?

(a)   0.5 watts
(b)   1 watt
(c)   4 watts
(d)   16 watts
(e)   256 watts

### QUESTION 14*

Suppose now that the capacitor is tuned to C = 1.25 μF. What is the net impedance Z of the circuit?

(a)   19 Ω
(b)   57 Ω
(c)   112 Ω
(d)   294 Ω
(e)   1061 Ω

### QUESTION 15**

You find two solenoids 1 and 2 with inductances L1 and L2. Solenoid 2 has half the diameter of solenoid 1, but twice the length and twice the number of turns of wire. Which one of the following statements on the inductances L1 and L2 of the solenoids is true?

(a)   L2 = L1 / 4
(b)   L2 = L1 / 2
(c)   L2 = L1
(d)   L2 = 2 L1
(e)   L2 = 4 L1

### QUESTION 16**

This question and the next one are conceptually related.

A circular loop is placed in a uniform external magnetic field B pointing into the page. The loop has resistance R.

The external magnetic field B is turned up slowly at a constant rate from 0 to 1 T in 100 s. Is there a current in the loop, and if so, in which direction does it flow?

(a)   clockwise
(b)   There is no current.
(c)   counterclockwise

### QUESTION 17*

The external magnetic field B is again turned up at a constant rate from 0 to 1 T, but now faster, in 10 s. Which one of the following statements about the EMF ε in the loop is true?

(a)   ε is 100 times smaller.
(b)   ε is 10 times smaller.
(c)   ε is the same.
(d)   ε is 10 times larger.
(e)   ε is 100 times larger

### QUESTION 18*

This question and the next one are conceptually related.

In the circuit shown below the resistor has a resistance of 5 Ω. The solenoid has 7 turns, a length of 10 cm and a radius of 1 cm. The battery supplies 10 volts to the circuit. Assume the battery has been connected for a long time.

Determine the value of the magnetic field B inside the solenoid after a time long enough for the circuit to achieve its maximum current.

(a)   B = 2.70 × 10-7 T
(b)   B = 9.34 × 10-5 T
(c)   B = 1.76 × 10-4 T
(d)   B = 3.33 × 10-2 T
(e)   B = 0.29 T

### QUESTION 19*

What is the value of the inductance L of the solenoid?

(a)   1.97 × 10-7 H
(b)   0.87 × 10-6 H
(c)   3.24 × 10-4 H
(d)   7.97 × 10-4 H
(e)   2.21 × 10-3 H

### QUESTION 20**

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

A rectangular loop of dimensions 3 cm × 5 cm is initially in a region having a uniform magnetic field of B = 3 T. The loop is being pulled out of this region into a region of no field at a rate of v = 10 m/s.

Consider a time interval beginning when the loop is well within the region of the magnetic field and ending when it is well into the field-free region. Over this interval, as a function of time, which graphs best represent the magnetic flux Φ and the induced EMF ε in the loop?

(a)   I
(b)   II
(c)   III

### QUESTION 21**

A rectangular loop of dimensions 3 cm × 5 cm is initially in a region having a uniform magnetic field of B = 3 T. The loop is pulled out of this region into a region of no field at a rate of v = 10 m/s, as shown below and as in previous problem.

Consider an instant during which the loop is partly out of the field region as shown above. If the resistance of the loop is 2 Ω, what is the magnitude of the current generated in the loop?

(a)   0.003 A
(b)   0.45 A
(c)   6.25 A
(d)   34 A
(e)   There is no current generated.

### QUESTION 22**

In the case of a current, in which direction does the current flow?

(a)   clockwise
(b)   counterclockwise
(c)   There is no current generated.

### QUESTION 23*

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

A single square loop of wire of side 0.2 m lies in the x-y plane. A current I = 3 A flows around the loop in a clockwise direction, as shown in the figure. A uniform magnetic field B of magnitude 0.75 T points along the +x direction.

What is the magnitude of the torque τ on the loop due to the magnetic field?

(a)   τ = 0.039 N·m
(b)   τ = 0.063 N·m
(c)   τ = 0.090 N·m

### QUESTION 24**

Which of these pictures best illustrates the direction the loop would rotate around an axis?

(a)   1
(b)   2
(c)   3
(d)   4
(e)   The loop does not rotate.

### QUESTION 25*

What is the magnitude of the torque if the magnetic field now points along the +z direction?

(a)   0 N·m
(b)   0.024 N·m
(c)   0.056 N·m

### QUESTION 26**

An inductor is made from a wire-wound cylindrical solenoid of radius 0.5 cm, length 7 cm, and contains 1000 turns of wire. A single loop of wire of radius 1 cm is centered around the inductor, as shown below. What is the mutual inductance M of the inductor on the loop? (Recall that Φs = M Ip.)

(a)   M = 0.038 μH
(b)   M = 0.27 μH
(c)   M = 1.4 μH

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.