### Spring 2008 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 126. The exam period was 90 minutes; the mean score was 97.4 the median was 100. 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**

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

For this and the next two questions, ignore all forces but the electrostatic.

Three charges (-q, -q, +3q) are located in the xy plane as shown in the figure.

How much work W is required to bring a charge +2q from infinity to position (x,y) = (d,0) for the charge configuration in this picture?

(a)   W = -4.45 J
(b)   W = -0.13 J
(c)   W = 0 J
(d)   W = +0.13 J
(e)   W = +4.45 J

### QUESTION 2*

What is the x-component of the force felt by the charge +2q in its new position?

(a)   Fx = -10.8 N
(b)   Fx = -7.6 N
(c)   Fx = 0 N
(d)   Fx = +7.6 N
(e)   Fx = +10.8 N

### QUESTION 3*

Remove the +3q from the charge configuration. What is the magnitude of the electric field E now felt by the charge +2q?

(a)   E = 0 N/C
(b)   E = 1.2 × 106 N/C
(c)   E = 2.4 × 106 N/C

### QUESTION 4*

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 (+/-).

Based on the map, what is the sign (+/-) of the charge q3?

(a)   -
(b)   0
(c)   +

### QUESTION 5*

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 6**

How much work W is required for you to move a charge of 1 C from point C to point D?

(a)   W = -4 J
(b)   W = -2 J
(c)   W = 0 J
(d)   W = +2 J
(e)   W = +4 J

### QUESTION 7*

What is the equivalent capacitance CAB measured between points A and B?

(a)   CAB = 9.2 μF
(b)   CAB = 22.2 μF
(c)   CAB = 25 μF
(d)   CAB = 50 μF
(e)   CAB = 90 μF

### QUESTION 8**

Two isolated identical conducting spheres have a charge of q and -3q, respectively. They are connected by a conducting wire, and after equilibrium is reached, the wire is removed (such that both spheres are again isolated). What is now the charge on each sphere?

(a)   q, -3q
(b)   -q, -q
(c)   0, -2q
(d)   2q, -2q
(e)   0, 0

### QUESTION 9*

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

The membrane of a living cell can be viewed as a parallel-plate capacitor. For a specific type of cell, the dielectric constant of the membrane is κ = 3, the width of the membrane is d = 7 nm (1 nm = 10-9 m) and total surface area of the membrane is A = 10-10 m2. The potential difference across the capacitor is maintained by charged ions.

What is the capacitance C of the cell membrane?

(a)   C = 1.9 × 10-9 F
(b)   C = 1.9 × 10-13 F
(c)   C = 3.8 × 10-13 F

### QUESTION 10***

At rest, the cell maintains a potential difference of 85 mV across the membrane. What is the number of ions N required to maintain this potential difference? (Assume the ions are singly charged and each has +/- the charge of an electron).

(a)   N = 3.2 × 10-14
(b)   N = 2.0 × 105
(c)   N = 6.2 × 1023

### QUESTION 11*

How much electrostatic energy U0 is stored in the cell membrane?

(a)   U0 = -1.4 × 10-15 J
(b)   U0= +1.4 × 10-15 J
(c)   U0 = 1.4 × 10-6 J

### QUESTION 12***

Assume that the cell membrane thins to half of its previous width, while the charges on both its sides remain the same. How would the original stored energy U0 compare to the new stored energy U' ?

(a)   U' = ½ U0
(b)   U' = U0
(c)   U' = 2U0

### QUESTION 13*

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

A capacitor array is shown in this figure. Each capacitor is identical with unknown capacitance C. An unknown potential difference V0 is maintained by a power supply. The equivalent capacitance of the network is 6 μF.

What is the capacitance C of each of the individual capacitors?

(a)   C = 2 μF
(b)   C = 4 μF
(c)   C = 6 μF
(d)   C = 9 μF
(e)   C = 12 μF

### QUESTION 14*

If the charge on the capacitor marked #1 at the bottom of the array is determined to be 21 μC, what is the unknown potential V0?

(a)   V0 = 0.8 V
(b)   V0 = 1.2 V
(c)   V0 = 3.5 V
(d)   V0 = 7.0 V
(e)   V0 = 9.0 V

### QUESTION 15***

If a dielectric material with κ = 8.3 is inserted between the plates of all the capacitors, the voltage across each capacitor

(a)   increases.
(b)   decreases.
(c)   remains the same.

### QUESTION 16*

With the dielectric still in place, a new battery is inserted in the place of the old one. The new battery maintains a potential difference of 40 V across the array. How much energy is stored in the capacitors after they are fully charged?

(a)   Utot = 40 mJ
(b)   Utot = 100 mJ
(c)   Utot = 140 mJ

### QUESTION 17**

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

In the circuit shown, the switch S has been open for a long time so that the capacitor is uncharged.

What is the current through the battery immediately after the switch is closed?

(a)   I (0+) = 0
(b)   I (0+) = V / (2R)
(c)   I (0+) = V / R

### QUESTION 18**

What is the current through the battery after the switch has been closed a long time?

(a)   I (∞) = 0
(b)   I (∞) = V / (2R)
(c)   I (∞) = V / R

### QUESTION 19***

What is the charge on the capacitor after the switch has been closed for a long time?

(a)   Q (∞) = CV / 2
(b)   Q (∞) = CV
(c)   Q (∞) = 2CV

### QUESTION 20*

After being closed for a long time, the switch is opened. How long does it take before the charge on the capacitor drops to 1/2 of the charge it has when the switch is opened? Assume that C = 4 μF, and R = 10 Ω.

(a)   t = 13.8 μs
(b)   t = 27.7 μs
(c)   t = 55.5 μs
(d)   t = 88.1 μs
(e)   t = 113.2 μs

### QUESTION 21**

This and the next question pertain to the following situation:

An isolated parallel plate capacitor contains charge Q0 = ±10 μC on its plates, corresponding to a potential difference of V0 = 10 V. The initial separation between the plates is d. Later, the distance between the plates is increased by a factor of two while the charge on each plate remains unchanged.

What is the voltage V' between the two plates after the separation becomes 2d?

(a)   V' = 2.5 V
(b)   V' = 5 V
(c)   V' = 10 V
(d)   V' = 20 V
(e)   V' = 40 V

### QUESTION 22**

Compare the energy U2d stored in the charged capacitor with plate separation 2d to the energy Ud stored in the charged capacitor with plate separation d.

(a)   [ U2d / Ud ] > 1
(b)   [ U2d / Ud ] = 1
(c)   [ U2d / Ud ] < 1

### QUESTION 23*

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

In the circuit shown below, the battery voltage is ε, the resistors R1 = R3 = R and R2 = R4 = 2R.

What is the equivalent resistance Req for this configuration of resistors?

(a)   Req = 5 R
(b)   Req = R / 10
(c)   Req = 3 R / 2
(d)   Req = 6 R / 5
(e)   Req = R

### QUESTION 24*

What is the total power P34 dissipated by resistors R3 and R4 combined?

(a)   P34 = ε2 / 10R
(b)   P34 = ε2 / R
(c)   P34 = ε2 / 5R
(d)   P34 = ε2 / 20R
(e)   P34 = ε2 / 3R

### QUESTION 25*

The battery voltage ε is 9 V and the current through the battery is 2 A. What is R ?

(a)   R = 3 Ω
(b)   R = 1 Ω
(c)   R = 10 Ω
(d)   R = 2 Ω
(e)   R = 0.1 Ω

### QUESTION 26*

Which one of the following choices is correct regarding the potential difference VAB = VA - VB between point A and point B?

(a)   VAB > 0
(b)   VAB < 0
(c)   VAB = 0

### QUESTION 27**

A lamp is connected in series with a resistor to a 12 V battery as in the circuit shown below. The lamp is designed to work when the voltage drop across it is 4 V and when it dissipates 12 W.

What should be the resistance R so that the lamp works as designed?

(a)   R = 0.12 Ω
(b)   R = 0.54 Ω
(c)   R = 2.67 Ω
(d)   R = 5.78 Ω
(e)   R = 98 Ω

### QUESTION 28*

A set of batteries and resistors is connected as shown here.

Which one of the following equations is correct?

(a)   ε1 + I1 R1 - ε2 + I1 R2 = 0
(b)   I1 - I2 = I3
(c)   -ε1 + I1 ( R1 + R2) + I3 R3 = 0

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.