### Fall 2008 Physics 102 Hour Exam 1(30 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 150. The exam period was 90 minutes; the mean score was 99.3 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**

Four charged particles are arranged in a square, as shown at the far right. Which of the arrows shown at right most closely shows the direction of the force acting on particle A?

(a)
(b)
(c)
(d)
(e)

### QUESTION 2**

Two identical positive charges of +Q are 1 m apart. What is the magnitude and direction of the electric field at point A, 0.25 m to the right of the left-hand charge? The answers are given in standard units.

(a)   3/4 kQ to the right
(b)   128/9 kQ to the left
(c)   160/9 kQ to the left
(d)   160/9 kQ to the right
(e)   128/9 kQ to the right

### QUESTION 3**

What is the change in potential energy of a particle of charge +q that is brought from a distance of 3r to a distance of 2r from a particle of charge -q?

(a)   kq2 / r
(b)   -kq2 / 6r
(c)   kq2 / 4r2
(d)   -kq2 / 4r2
(e)   kq2 / r2

### QUESTION 4**

A parallel plate capacitor has area A and separation d. Two different dielectrics each fill half the space between the plates of a parallel-plate capacitor as shown below. Determine a formula for the capacitance in terms of K1, K2, the area A of the plates, and the separation d.

(a)
(b)
(c)
(d)
(e)

### QUESTION 5**

This and the next question pertain to the following situation:

Consider the three positive charges in the configuration shown.

How much electrostatic potential energy does this system have?

(a)   U = 23.0 kQ2 / d
(b)   U = 21.5 kQ2 / d
(c)   U = 0
(d)   U = 14.5 kQ2 / d2
(e)   U = -25.0 kQ2 / d

### QUESTION 6*

Where could you move the charge Q so it feels no net force (besides infinitely far away)?

(a)   0.56d to the right of the 5Q charge
(b)   0.56d to the left of the 5Q charge
(c)   d/2 to the right of the 5Q charge

### QUESTION 7***

This and the next question pertain to the following situation:

Two small spheres with equal unknown mass are suspended by light-weight strings of length 12 cm. When a charge of +3 nC is placed on each sphere, each string makes an angle of 20° with the vertical in equilibrium.

What is the mass of each ball?

(a)   1.21 × 10-6 kg
(b)   3.37 × 10-6 kg
(c)   1.07 × 10-5 kg
(d)   1.35 × 10-5 kg
(e)   2.23 × 10-5 kg

### QUESTION 8**

If an electric field pointing up is applied to the charges, the angle between the strings will

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

### QUESTION 9*

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

Four capacitors are connected as shown below. A 15 V battery is centered in the circuit. Assume that all of the capacitors are fully charged and that no current is flowing.

What is the charge on one of the plates of the 4 μF capacitor?

(a)   Q4 = 15 μC
(b)   Q4 = 30 μC
(c)   Q4 = 60 μC

### QUESTION 10**

Compute the total stored energy in the capacitors.

(a)   Utot = 0.05 × 10-3 J
(b)   Utot = 1.46 × 10-3 J
(c)   Utot = 0.75 × 10-4 J
(d)   Utot = 1.1 × 10-4 J
(e)   Utot = 3.1 × 10-4 J

### QUESTION 11**

If you place a dielectric with κ = 7.5 between the plates of the 1 μF capacitor (at the top), the charge on the other three (unmodified) capacitors would

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

### QUESTION 12*

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

Given is a map of equal-potential lines (see figure below). The potential is created by three charges in a plane (q1, q2, q3). Potential values are given in volts. Note the signs (+/-).

What is the sign (+/-) of the charge q2?

(a)   -
(b)   0
(c)   +

### QUESTION 13*

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

(a)   left
(b)   right
(c)   up
(d)   down
(e)   cannot be determined

### QUESTION 14*

How much work W by an external force is required to move a charge of 1 C from point C to point D?

(a)   W = -4 J
(b)   W = -3 J
(c)   W = 0 J
(d)   W = +3 J
(e)   W = +4 J

### QUESTION 15*

This and the next question pertain to the following situation:

Three capacitors are connected to a battery as shown in the diagram. The potential difference provided by the battery is 24 volts, while C1 = 8 μF, C2 = 6 μF and C3 = 4 μF.

What is Q1, the charge on the capacitor C1?

(a)   Q1 = 6.0 × 10-5 C
(b)   Q1 = 8.4 × 10-5 C
(c)   Q1 = 10.8 × 10-5 C
(d)   Q1 = 14.4 × 10-5 C
(e)   Q1 = 19.2 × 10-5 C

### QUESTION 16***

What is V3, the potential difference across the plates of capacitor C3?

(a)   V3 = 4.8 V
(b)   V3 = 6.0 V
(c)   V3 = 9.6 V
(d)   V3 = 12.0 V
(e)   V3 = 14.4 V

### QUESTION 17*

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

Compare I2 (the current through R2) with I3 (the current through R3).

(a)   I2 > I3
(b)   I2 = I3
(c)   I2 < I3

### QUESTION 18**

Compare V3 (the voltage across R3) with V4 (the voltage across R4).

(a)   V3 > V4
(b)   V3 = V4
(c)   V3 < V4

### QUESTION 19*

How much power is being delivered by the battery?

(a)   P = 1.95 W
(b)   P = 5.32 W
(c)   P = 11.9 W
(d)   P = 25.8 W
(e)   P = 30.8 W

### QUESTION 20**

What is I2, the current through R2?

(a)   I2 = 0.232 A
(b)   I2 = 0.387 A
(c)   I2 = 0.459 A
(d)   I2 = 0.521 A
(e)   I2 = 0.692 A

### QUESTION 21***

This and the next question pertain to the following situation:

Five resistors and three batteries are connected, as shown. Define the currents I1 through I4 with the directions given by the arrows.

Which one of these equations is valid?

(a)   I1 + I2 + I3 - I4 = 0
(b)   I1 + I2 + I3 + I4 = 0
(c)   I1 - I2 - I3 - I4 = 0

### QUESTION 22**

Which one of these equations is not valid?

(a)   VA - I1R1 + I4R4 = 0
(b)   VC + I2R2 - VB + I2R5 - I3R3 = 0
(c)   VC - I4R4 + I3R3 = 0

### QUESTION 23*

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

In the circuit shown, a switch can connect the top plate of the capacitor to either point A or point B. Assume that the switch was originally left at B for a very long time so that the capacitor is initially uncharged. Then at time t = 0, the switch is flipped over to connect to point A.

What is the current through the battery immediately after the switch is moved to position A?

(a)   I(0+) = 0
(b)   I(0+) = Vb / 40
(c)   I(0+) = Vb / 20
(d)   I(0+) = Vb / 10
(e)   I(0+) = Vb / 5

### QUESTION 24*

What is the current through the battery a long time after the switch is moved to position A?

(a)   I = 0
(b)   I = Vb / 40
(c)   I = Vb / 20
(d)   I = Vb / 10
(e)   I = Vb / 5

### QUESTION 25**

Let tA be the time it takes the current into the capacitor to fall to 1/e of its initial value once the switch is in position A. After having left it at A a long time, you flip the switch back to B. Let tB be the time it takes the current through the capacitor to fall to 1/e of the value it has just after the switch is flipped to B. Which of the following is true?

(a)   tA < tB
(b)   tA = tB
(c)   tA > tB

### QUESTION 26**

A doped semiconductor has a resistivity of ρ = 10-3 Wm. If a 1 micrometer thick slab of this material is to be cut into a resistor equaling 100 W, what dimensions should be chosen? (Note: the figure shown is not necessarily to scale.)

(a)   w = 10 μm and L = 1 μm
(b)   w = 1 μm and L = 1 μm
(c)   w = 1 μm and L = 100 μm
(d)   w = 0.1 μm and L = 100 μm
(e)   w = 100 μm and L = 1 μm

### QUESTION 27**

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

A circuit consisting of resistors and a battery is shown. The battery voltage is V = 12 volts. The resistances shown in the diagram are all in ohms.

The magnitude of the current I through the leftmost 4 ohm resistor is:

(a)   2.0 A
(b)   3.0 A
(c)   3.4 A
(d)   6.0 A
(e)   9.0 A

### QUESTION 28*

The three resistors to the right of a line through P and Q are removed (the 4, 4, and 8 ohm resistors), and are replaced by a single resistor that is connected between points P and Q in the circuit. The current that passes through the battery is the same with this new resistor, as it was before the three resistors were replaced. What is the resistance of the single, new resistor?

(a)   2.0 ohms
(b)   4.0 ohms
(c)   6.7 ohms
(d)   8.0 ohms
(e)   16.0 ohms

### QUESTION 29**

How much current flows through the battery?

(a)   1 A
(b)   2 A
(c)   3 A
(d)   4 A
(e)   12 A

### QUESTION 30**

How much power is provided to the resistors by the battery?

(a)   12 watts
(b)   24 watts
(c)   36 watts
(d)   48 watts
(e)   144 watts

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.