### Spring 2010 Physics 102 Hour Exam 1(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 122. The exam period was 90 minutes; the mean score was 84.4 the median was 85. 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*

A closed circuit consists of a battery connected to a 50 Ω resistor. The 50 Ω resistor is rated to ¼ W, meaning that it will burn out if the power dissipated exceeds ¼ W. What is the maximum possible voltage of the battery?

(a)   3.54 V
(b)   12.5 V
(c)   200 V

### QUESTION 2***

A parallel plate capacitor has an area A and separation d. Two different dielectrics each fill half the space between the plates of the capacitor as shown. Express the capacitance of this capacitor in terms of the dielectric constants K1, K2, the area A of the plates and the separation d.

(a)
(b)
(c)

### QUESTION 3*

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

A lightning cloud-ground system can be modeled as a parallel plate capacitor. The cloud capacitor has capacitance = 2.27 × 10-6 F. The cloud is hovering at a height h = 1 km above the ground level. Think of the ground beneath the cloud as the other plate of the capacitor.

What is the area of a capacitor plate in this cloud-ground system?

(a)   2.56 × 102 km2
(b)   5.20 × 103 km2
(c)   3.91 × 108 km2

### QUESTION 4**

For lightning to occur, the electric field underneath the cloud must be greater than E = 1 kV/cm. What is the minimum charge required in the cloud for lightning to strike?

(a)   3.62 × 10-2 C
(b)   1.32 × 102 C
(c)   2.27 × 102 C
(d)   5.79 × 104 C
(e)   3.62 × 103 C

### QUESTION 5**

A charged insulator and a conductor with net charge = 0 near each other

(a)   attract each other electrically.
(b)   repel each other electrically.
(c)   atract or repel, depending on the sign of the charge.

### QUESTION 6**

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

A circuit has a 5 V battery, two resistors with values indicated below and a capacitor. There is a current I through the battery, I1 through the capacitor and I2 through resistor R1.

What is the value of the current I1 right after the switch is closed? (There is no charge on the capacitor.)

(a)   0 A
(b)   1.10 A
(c)   1.67 A
(d)   2.33 A
(e)   9.31 A

### QUESTION 7*

What is the value of the current I1 after a long time?

(a)   0 A
(b)   1.67 A
(c)   2.5 A
(d)   3.2 A
(e)   4.17 A

### QUESTION 8***

At some intermediate time the charge on the capacitor is found to be equal to 4 μC. What is the value of the current I at that moment?

(a)   0.10 A
(b)   0.43 A
(c)   0.50 A
(d)   0.67 A
(e)   1.33 A

### QUESTION 9**

This question and the next one pertain to this situation.

A singly-ionized gold atom (mass = 3.27 × 10-25 kg, charge = +1.6 × 10-19 C) is placed precisely onto the center of a one- meter track. A uniform electric field of 5 × 106N/C is now turned on which points in the same direction as the track. The particle is accelerated to the end of the track where its velocity is measured. This velocity is discovered to be:

(a)   1.56 × 106 m/s
(b)   2.21 × 106 m/s
(c)   3.13 × 106 m/s

### QUESTION 10*

In a second experiment, the gold ion is replaced by a single electron. Which of these properties will stay the same?

(a)   the speed of the particle when it exits the electric field
(b)   the direction the particle moves
(c)   the magnitude of the force on the particle

### QUESTION 11***

Shown in the diagram are two charges each with mass 1 kg. One is held at a fixed position while the other is free to move. Initially they are separated by a distance of 2 m. At t = 0 the charge on the right is released from rest. What is the speed of the charge on the right after a very long time?

(a)   1.5 × 105 m/s
(b)   2.1 × 105 m/s
(c)   3.4 × 105 m/s
(d)   4.7 × 105 m/s
(e)   6.7 × 105 m/s

### QUESTION 12*

Refer to the diagram shown below. Each resistor in the diagram has the same resistance value. Which single resistor A, B or C would you remove and replace with a conducting wire to yield the smallest equivalent resistance R ?

(a)   resistor A
(b)   resistor B
(c)   resistor C

### QUESTION 13**

This question and next two pertain to the following situation:

Two charges are located as in the figure on the right and are equidistant from line B.

If two charges have the same amount of charge with the same sign, where is the electric field zero?

(a)   at point A
(b)   on Line B
(c)   nowhere

### QUESTION 14**

If the absolute values of the two charges are the same but the left charge is positive and the right charge is negative, where is the electric field zero?

(a)   at point A
(b)   on Line B
(c)   infinitely far away

### QUESTION 15*

The two charges now have identical negative charges. If a positive test charge is located at the origin and is then bumped upward, just a little, along line B, the test charge will

(a)   pick up acceleration in the upward line B direction and escape.
(b)   begin a circular orbit.
(c)   will oscillate up and down along the line B direction at point A.

### QUESTION 16*

This question and next one pertain to the following situation:

Object A hangs from an insulated thread. When object B, which has a charge of +130 nC, is held fixed nearby, A is attracted to it. In equilibrium, object A hangs at an angle θ = 7.20° with respect to the vertical and 5.00 cm left of B. The absolute value of the amount of charge for object A is 238 nC.

Would object A be positively or negatively charged?

(a)   positive only
(b)   negative only
(c)   The sign doesn't matter.

### QUESTION 17**

What is the mass of the object A?

(a)   882 g
(b)   450 g
(c)   90 g
(d)   10 g
(e)   1.47 g

### QUESTION 18*

What is the equivalent capacitance of the following capacitor network? Each capacitor in the network is 10 μF.

(a)   921 pF
(b)   438 nF
(c)   1.32 μF
(d)   2.50 μF
(e)   5.03 μF

### QUESTION 19*

A positive test charge is placed on the X (origin) of the following graph with initial speed = 0 and is then released. In which direction will the charge start to move? All charges in the diagram are either +3.0 coulombs, or -3.0 coulombs. The charges are located at the following points, as indicated below in the diagram.

(x,y) : (-a,b), (-a,-b), (a,b), (a,-b), (0,c), (0,-c)

(a)   north
(b)   south
(c)   east
(d)   west
(e)   It wouldn't move

### QUESTION 20**

Suppose a resistor R of resistance 2560 Ω and a capacitor C of 3.9 mF are in series. A switch connects the resistor to the capacitor. The capacitor is initially fully charged. After 30 seconds of time, what fraction of the initial charge is left?

(a)   0.0496
(b)   0.2444
(c)   0.4582
(d)   0.7847
(e)   1.000

### QUESTION 21**

A parallel plate capacitor has area A1 and no dielectric between its plates. It is maintained at a potential difference of 23 V. Next a polystyrene cylinder (κ = 2.6) with cross-sectional area A2 < A1 is inserted in between the plates from one plate to the other. The voltage is kept fixed. How is the capacitor's stored energy affected?

(a)   The energy increases.
(b)   The energy deceases.
(c)   The energy remains the same.

### QUESTION 22**

A space heater capable of producing 1000 W of heat has a cylindrical heating element that is 1 cm in diameter and 6 cm long. Assuming a constant voltage of 120 V, estimate the resistivity of the heating element material.

(a)   0.002 Ω*m
(b)   0.019 Ω*m
(c)   0.056 Ω*m
(d)   0.075 Ω*m
(e)   0.134 Ω*m

### QUESTION 23***

There is an electric field with magnitude 2 V/m pointing in the +x direction. A particle with charge +1 μC initially sits at (x,y) = (1 m, 0 m). A force is exerted on the particle to move it to (2 m, 0 m). Next the particle is moved to (3.5 m, 4 m). Finally the particle is moved to (2 m, 3 m). What is the total work done by the electric field?

(a)   -4.0 μJ
(b)   -2.0 μJ
(c)   0 J
(d)   +2.0 μJ
(e)   +4.0 μJ

### QUESTION 24**

This question and next one pertain to the following situation:

Consider the configuration of batteries and resistors depicted below. The batteries have potential differences of ε1 = 2 V, ε2 = 5 V, ε3 = 4 V. The resistors have resistances R1 = 10 Ω, R2 = 5 Ω, R3 = 20 Ω, R4 = 10 Ω.

What is the absolute value of the potential difference between points A and B?

(a)   0 V
(b)   2 V
(c)   4 V

### QUESTION 25*

Which one of the following is NOT a valid Kirchhoff loop equation?

(a)   - ε1 + I2 R2 - I3R3+ I1R1 = 0
(b)   - ε1 + ε2 + I1R1 = 0
(c)   + ε3 + I2 R2 = 0

### QUESTION 26*

This question and the next two pertain to this situation.

Below is an equipotential map generated by three charges (q1, q2, q3). The value on each equipotential line is in volts. Note the signs (+/-).

Based on this map, answer these three questions.

What is the approximate direction of the electric field at point B?

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

### QUESTION 27*

What is the sign of charge q1?

(a)   positive
(b)   negative

### QUESTION 28**

What is the work W done by you in moving a 1 μC charge from point A to point B to point C?

(a)   W = -2 μJ
(b)   W = -1 μJ
(c)   W = 0 μJ
(d)   W = 1 μJ
(e)   W = 2 μJ

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.