### Fall 2006 Physics 102 Hour Exam 1(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 124. The exam period was 90 minutes; the mean score was 99.3 the median was 103. Click here to see 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**

The resistivities for Lead (Pb) and Chromium (Cr) are ρPb = 0.21 μΩ-m and ρCr = 0.13 μΩ-m respectively. A Lead wire 1 m long with diameter 1 mm is found to have the same resistance as a Chromium wire that is also 1 m long. What is the diameter of the Chromium wire?

(a)   0.38 mm
(b)   0.62 mm
(c)   0.79 mm
(d)   1.27 mm
(e)   1.62 mm

### QUESTION 2**

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

In the circuit shown below, three identical bulbs are wired to a battery.

The voltage drop across Bulb 1 is the same as the voltage drop across Bulb 3.

(T)   True
(F)   False

### QUESTION 3*

The current through Bulb 1 is the same as the current through Bulb 2.

(T)   True
(F)   False

### QUESTION 4*

The total current flowing through the battery is

(a)   2.7 A
(b)   8.0 A
(c)   12.0 A
(d)   85.3 A
(e)   384.0 A

### QUESTION 5*

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

The illustrated circuit contains two batteries, three resistors, and two switches.

At time t = t1 switch S1 is closed (so that current flows through the switch) and S2 is opened. What is the current I1?

(a)   0.60 A
(b)   1.50 A
(c)   2.86 A

### QUESTION 6*

At time t = t2 switch S2 is closed (so that current flows through the switch) while S1 is opened. What is the current I2 that flows after the switch is closed?

(a)   0.57 A
(b)   0.72 A
(c)   1.14 A

### QUESTION 7**

At time t = t12 both switches S1 and S2 are closed so that current flows through both of the switches. What is the current I3?

(a)   0.85 A
(b)   0.29 A
(c)   2.00 A
(d)   0.57 A
(e)   0.72 A

### QUESTION 8*

In this diagram a circuit fragment is built from ten identical 12 Ω resistors. What is the resistance between the points labeled A and B?

(a)   15 Ω
(b)   25 Ω
(c)   48 Ω
(d)   72 Ω
(e)   120 Ω

### QUESTION 9*

A square, parallel plate capacitor with side length L = 30 cm and separation 2 mm is filled completely with a dielectric with κ = 2.4. What is its capacitance?

(a)   4.02 mF
(b)   1.56 μF
(c)   9.56 × 10-10 F

### QUESTION 10**

Which one of the following statements is true?

(a)   The units of the electric field are equivalent to Newtons per Volt.
(b)   The units of capacitance are equivalent to Coulombs per Newton.
(c)   The units of the electrostatic potential are equivalent to Coulombs per Farad.

### QUESTION 11*

This and the next question pertain to the following situation:

In the following diagram C1 = C2 = C3 = C4 = 10 μF. Initially the gap between the capacitors is empty of any material.

What is the total capacitance between points A and B?

(a)   0.014 μF
(b)   0.72 μF
(c)   1.2 μF
(d)   2.0 μF
(e)   6.0 μF

### QUESTION 12*

Capacitor C3 is then filled with Barium Titanate, a dielectric with κ = 6000. What is the total capacitance between points A and B now?

(a)   1.68 μF
(b)   0.168 μF
(c)   6.67 μF
(d)   0.091 μF
(e)   24.2 μF

### QUESTION 13**

A point charge Q1 = 5 μC is held fixed at the origin. A second charge Q2 = 2 μC is placed a distance d1 = 5 mm away. How much work would be required for you to move Q2 to a distance d2 = 8 mm away from the origin? Be careful about the sign.

(a)   3.68 J
(b)   6.75 J
(c)   -6.75 J
(d)   -3.68 J
(e)   1.07 J

### QUESTION 14*

Two charged beads, Q1 and Q2, are placed on a long frictionless (insulating) rod. Initially they are very far apart; the bead Q2 is glued in place and does not move. Both beads have mass 10 g and carry charge 2 μC. Q1 is set in motion at a velocity v = 10 m/s towards Q2.

How close does Q1 get to Q2 before reversing its direction of motion? Recall that an object’s initial kinetic energy is mv2/2.

(a)   1.4 m
(b)   72 mm
(c)   825 μm

### QUESTION 15**

A circuit is made from a 12 V battery and three capacitors with capacitances 2 μF, 4 μF, and 6 μF as shown in this figure. What is the voltage difference between the point labeled “A” and the point labeled “0 V” in the circuit?

(a)   2.00 V
(b)   6.55 V
(c)   10.00 V
(d)   4.00 V
(e)   2.44 V

### QUESTION 16**

This and the next question pertain to the following situation:

Three charges, Q1, Q2, and Q3, are arranged on a square of side length d, as shown in the figure. Q1 = 5 μC, Q2 = Q3 = -2 μC and d = 2 m.

What is the value of the electrostatic potential at point A?

(a)   -8.4 kV
(b)   8.4 kV
(c)   2.1 kV
(d)   -2.1 kV
(e)   4.2 kV

### QUESTION 17*

If the distance d were doubled to 4 m what would happen to the potential at point A? Assume Q1, Q2, Q3, and A are all located on the corners of the larger square. The potential at A would

(a)   double.
(b)   decrease by a factor of two.
(c)   not change.
(d)   increase by a factor of four.
(e)   decrease by a factor of four.

### QUESTION 18*

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

Three charges (a, b, and c) are fixed at (-4, 0), (0,4), and (+4,0) as shown in the figure: qa = +2μC, qb = -3μC, and qc = +2μC. The grid spacing is one meter.

What is the magnitude of the force that charge b exerts on charge c?

(a)   0.03 N
(b)   2.76 N
(c)   1.69 mN
(d)   0.32 mN
(e)   0.73 N

### QUESTION 19*

What is the direction of the electric field at the origin (0,0) due to all three charges?

(a)   pointing up
(b)   pointing down
(c)   pointing to the left
(d)   pointing to the upper right
(e)   pointing to the lower left

### QUESTION 20*

How would the magnitude of the electric field change at the origin (0,0) if each of the charges was moved twice as far from the origin?

(a)   The magnitude of the electric field would increase by a factor of four.
(b)   The magnitude of the electric field would double.
(c)   The magnitude of the electric field would be unchanged.
(d)   The magnitude of the electric field would decrease by a factor of two.
(e)   The magnitude of the electric field would decrease by a factor four.

### QUESTION 21*

What are the x,y components of the total force acting on charge a?

(a)   Fx = 0.6325 mN  and  Fy = 1.195 mN
(b)   Fx = 1.333 mN  and  Fy = -1.23 mN
(c)   Fx = 2.03 N  and  Fy = 0.23 N
(d)   Fx = 0  and  Fy = 0.234 mN
(e)   Fx = -30.0 mN  and  Fy = 12.0 mN

### QUESTION 22*

The following figure shows a pattern of electric field lines. Compare the magnitude of the electric field at points A and B.

(a)   A = B
(b)   A > B
(c)   A < B

### QUESTION 23*

This and the next question pertain to the following situation:

A hollow conducting cylinder is held fixed between two conducting spheres that are also fixed in space. The upper sphere contains positive charge, while the lower sphere contains an equal amount of negative charge. The total charge of the conducting cylinder is zero. The cylinder is insulated from the ground.

Which figure shows the correct pattern of field lines?

(a)
(b)
(c)

### QUESTION 24*

If the hollow cylinder is moved towards the sphere containing negative charge, how would the magnitude of the electric field at the center of the cylinder change? (Recall that the cylinder is a conductor.)

(a)   The magnitude of the electric field would increase.
(b)   The magnitude of the electric field would decrease.
(c)   The magnitude of the electric field would remain the same.

### QUESTION 25**

This and the next question pertain to the following situation:

A neutral conducting sphere is placed on a frictionless plate midway between two fixed unequal point charges: qL = +5μC and qR = +1μC. The sphere is free to move and is insulated from the ground.

In which direction do you expect the sphere to move?

(a)   to the left
(b)   to the right
(c)   The sphere will not move.

### QUESTION 26***

In which direction would you expect the sphere to move if it were made instead of a dielectric insulator, for example, paper or plastic?

(a)   to the left
(b)   to the right
(c)   The sphere would not move.

### QUESTION 27*

Four charges, each with Q = 3 μC, are brought in from infinitely far away to be fastened to the vertices of a square of side length 1 m as shown in the figure. How much work is required to assemble this system of charges?

(a)   0.41 J
(b)   0.081 J
(c)   0.44 J
(d)   1.41 J
(e)   0.12 × 10-10 J

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.