### Fall 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 125. The exam period was 90 minutes; the mean score was 79.2 the median was 79. 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 question and the next three pertain to this situation.

A circuit consists of a 6 V battery, 3 resistors and 2 capacitors as depicted below. Both capacitors are initially uncharged. Switch S1 is then closed at time t = 0. Switch S2 remains open until stated otherwise.

What is the voltage V1 across C1 right when S1 is closed (at t = 0)?

(a)   V1 = 0 V
(b)   V1 = 2 V
(c)   V1 = 4 V

### QUESTION 2***

What is the power P dissipated from R2 right when S1 is closed (at t = 0)?

(a)   P = 0 W
(b)   P = 0.12 W
(c)   P = 0.24 W
(d)   P = 0.72 W
(e)   P = 1.2 W

### QUESTION 3**

At a later time (S2 is still open) the charge on C1 is found to be 6 μC. How much current I3 is going through R3 at that moment?

(a)   I3 = 0 A
(b)   I3 = 0.3 A
(c)   I3 = 0.6 A
(d)   I3 = 0.8 A
(e)   I3 = 1.6 A

### QUESTION 4**

Now S2 is closed and a long time has elapsed to charge the appropriate capacitor(s) to maximum capacity. A total of 30 μC of charge are found on C1 and C2 combined. What is the capacitance C2?

(a)   C2 = 2 μF
(b)   C2 = 3 μF
(c)   C2 = 4 μF
(d)   C2 = 6 μF
(e)   C2 = 12 μF

### QUESTION 5*

This question and the next one pertain to the circuit shown here.

What is the equivalent resistance Req of the circuit?

(a)   Req = 5R/6
(b)   Req = 7R/6
(c)   Req = 6R/5
(d)   Req = 36R/13
(e)   Req = 5R

### QUESTION 6***

What is the magnitude of the potential difference between points A and B, ΔV ?

(a)   ΔV = 4 V
(b)   ΔV = 4.8 V
(c)   ΔV = 8 V

### QUESTION 7***

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

A circuit consists of a battery, a capacitor and two resistors in the configuration shown below. Initially, the switch is open and the capacitor is uncharged. The values associated with the parameters of the circuit are ε = 12 V, C = 3 μF, R1 = 22 Ω and R2 = 15 Ω.

The switch is closed and the capacitor is allowed to charge. When the charge on the capacitor reaches 10 μC, what is the current I1 through R1?

(a)   I1 = 0.00 A
(b)   I1 = 0.15 A
(c)   I1 = 0.22 A
(d)   I1 = 0.32 A
(e)   I1 = 0.39 A

### QUESTION 8**

After a long time, the switch is opened again. What is the current I2 through R2? You may assume that the capacitor is fully charged.

(a)   I2 = 0.023 A
(b)   I2 = 0.32 A
(c)   I2 = 1.20 A
(d)   I2 = 1.67 A
(e)   I2 = 3.10 A

### QUESTION 9*

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

You are given a circuit consisting of five capacitors and a battery, as shown.

What is the total equivalent capacitance Ceq of the circuit?

(a)   Ceq = 1.7 μF
(b)   Ceq = 7.6 μF
(c)   Ceq = 12.8 μF

### QUESTION 10***

What is the charge Q3 on C3?

(a)   Q3 = 12.7 μC
(b)   Q3 = 18.3 μC
(c)   Q3 = 27.5 μC
(d)   Q3 = 31.8 μC
(e)   Q3 = 45.8 μC

### QUESTION 11*

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

Four charges are placed at the corners of a rectangle with sides of length 3 cm and 4 cm as shown below.

What is the direction of the electric field at the center of the rectangle due to these charges?

(a)   in the +x direction
(b)   in the +y direction
(c)   in the -y direction

### QUESTION 12**

What is the magnitude of the electric field at the center of the rectangle due to these charges?

(a)   |E| = 2.56 × 105 N/C
(b)   |E| = 34.6 × 106 N/C
(c)   |E| = 1.38 × 108 N/C
(d)   |E| = 2.93 × 109 N/C
(e)   |E| = 16.5 × 109 N/C

### QUESTION 13**

How much work in total do you need to do to bring a charge of 3.9 nC from far away first to point A, which is the midpoint of the 3 cm side, then to point B, which is the midpoint of the 4 cm side, and finally to the center?

(a)   Wtotal = 0 J
(b)   Wtotal = 10 J
(c)   Wtotal = 30 J
(d)   Wtotal = 45.5 J
(e)   Wtotal = 125 J

### QUESTION 14**

An electron (charge -1.6 × 10-19 C) travels along the path shown below from point A to point B through a constant upwards electric field E = 2 N/C. What is the work done by the field Wfield ?

(a)   Wfield = 3.20 × 10-19 J
(b)   Wfield = 0.75 × 10-19 J
(c)   Wfield = 0 J
(d)   Wfield = -3.88 × 10-17 J
(e)   Wfield = -5.23 × 10-17 J

### QUESTION 15***

In general, if at some point in space the electric field is 0 N/C, does this imply that the electric potential is 0 V ?

(a)   Yes
(b)   No

### QUESTION 16**

What is the equivalent capacitance Ceq of this circuit (in terms of C0) ?

(a)   Ceq = 4 C0
(b)   Ceq = 4 C0 / 3
(c)   Ceq = 3 C0 / 4
(d)   Ceq = C0 / 4
(e)   none of the above

### QUESTION 17*

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

A fixed, conducting sphere A has a net positive charge. A second conducting sphere B that hangs from the ceiling is placed to the right of the fixed sphere A, as shown in the figure. Sphere B has NO net charge. Assume the spheres are ideal conductors.

The electric force between spheres A and B is

(a)   repulsive.
(b)   attractive.
(c)   zero.

### QUESTION 18*

Next the fixed sphere A is replaced with one that has a net negative charge. The electric force between sphere A and B is

(a)   repulsive.
(b)   attractive.
(c)   zero.

### QUESTION 19*

Now the hanging sphere B is replaced with a perfect insulating sphere with no net charge. The fixed sphere A has a net negative charge. The electric force between the two spheres is

(a)   repulsive.
(b)   attractive.
(c)   zero.

### QUESTION 20**

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

This is a map of equipotential lines for two charges Q1 and Q2. Potential values are accurate and given in volts.

Which one of the following statements about the magnitudes of the charges is true?

(a)   |Q1| > |Q2|
(b)   |Q1| = |Q2|
(c)   |Q1| < |Q2|

### QUESTION 21**

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

(a)   up
(b)   down
(c)   right
(d)   left
(e)   pointing towards charge Q2

### QUESTION 22**

A +2 μC charge is moved from point A to point B. What is the change in its electric potential energy ΔU = UB - UA?

(a)   ΔU = -2 μJ
(b)   ΔU = 0 μJ
(c)   ΔU = 2 μJ

### QUESTION 23*

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

A capacitor is composed of two parallel plates of area 5 × 10- 4m2 separated by a distance 7 × 10-4m as shown below.

Consider the situation when the capacitor is in isolation and charged to maximum capacity. The electric field in this situation is 2 × 106 V/m.

What is the charge Q on one of the plates of the capacitor?

(a)   Q = 6.89 × 10-12 C
(b)   Q = 8.85 × 10-9 C
(c)   Q = 4.67 × 10-6 C

### QUESTION 24*

A charged particle of charge 3 × 10-19 C and mass 2.4 × 10-10 kg is placed at the central point marked 'O' without redistributing any of the charges on the capacitor and is then released. Upon release, assuming that the effects of gravity can be neglected, the particle

(a)   accelerates to the right at 0.0025 m/s2.
(b)   accelerates to the left at 0.382 m/s2.
(c)   remains motionless since it is the equilibrium point.

### QUESTION 25***

Now consider a slab of dielectric constant κ = 3.2 inserted in between the plates as shown in situation B above. Compared to the situation having no dielectric present, how do i) the voltage V across the plates and ii) the stored potential energy U change?

(a)   Both V and U increase.
(b)   V increases and U decreases.
(c)   V decreases and U increases.
(d)   Both V and U decrease.
(e)   Both stay the same.

### QUESTION 26*

A fully charged capacitor with C = 6.33 × 10-12 F, a resistor with resistance R = 103 Ω and a switch S are in a circuit as shown above. At t = 0 the switch is closed. The charge on the capacitor decreases to one fifth of its maximum charge at what time t5?

(a)   t5 = 2.87 × 10-12 s
(b)   t5 = 1.02 × 10-8 s
(c)   t5 = 3.51 × 10-4 s
(d)   t5 = 1.32 s
(e)   t5 = 6.44 × 104 s

### QUESTION 27*

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

Four resistors and two batteries are connected as shown below. The corresponding resistances and voltages have the values R1 = R2 = R3 = R4 = 2 Ω and ε1 = ε4= 4 V. Define currents I using the directions given by the arrows.

When the switch S is in the 'open' position (as shown), what is the value of the current I23?

(a)   I23 = 0.5 A
(b)   I23 = 1.33 A
(c)   I23 = 6.75 A

### QUESTION 28*

When the switch S is in the 'closed' position, which one of these equations is valid?

(a)   ε1 - I1R1 + I2R2 = 0
(b)   I1 + I23 - I4 = 0
(c)   ε1 - I1R1 + I4R4 - ε4 = 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.