Spring 2006 Physics 102 Hour Exam 1
(26 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 103. The exam period was 90 minutes; the mean score was 80.7 the median was 83. Click here to see the formula sheet that came with the exam.

Some helpful information:
• 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 conducting sphere of an electroscope is loaded with charge q so that the conducting leaves stand apart as shown in Figure I. As a rod with charge QA is brought near (but does not touch) the conducting sphere in figure II, the leaves move towards one another. This rod is removed and a different rod holding charge QB is brought near the conducting sphere in Figure III. The leaves are seen to move farther apart than in Figure I.

Which one of the following statements must be true?

(a)   The magnitude of QA is less than the magnitude of q.
(b)   QA and q have the same sign.
(c)   QB and q have the same sign.
(d)   QA is positive and QB is negative.
(e)   QA is negative and QB is positive.


QUESTION 2*

The electric field inside a conductor is

(a)   always oriented parallel to the local gravitational field.
(b)   zero.
(c)   generally oriented perpendicular to any externally applied magnetic field


QUESTION 3*

After the switch is closed in this circuit, what is the current through the 10 Ω resistor?

(a)   0.143 A
(b)   0.200 A
(c)   0.429 A


QUESTION 4**

In this cicuit, how much power is dissipated by the 20 Ω resistor?

(a)   1.67 W
(b)   5.00 W
(c)   7.50 W


QUESTION 5**

In this circuit, what is the current though resistor R3?

(a)   0.02 A
(b)   0.08 A
(c)   0.10 A
(d)   0.71 A
(e)   1.70 A


QUESTION 6**

In this circuit, the battery voltages E1 and E2 are unknown. In order for the current through the 20 Ω resistor to be zero, the relationship between E1 and E2 must be which of the following?

(a)   E1 = 0.5 E2
(b)   E1 = E2
(c)   E1 = 2 E2


QUESTION 7*

This and the next question concern a soon-to-be-bankrupt elevator company.

Engineers at Nillog Lifts, Inc. design an elevator that uses a pair of positive charges Q = 0.1 C for propulsion. One is placed at the bottom of the elevator shaft, the other fixed to the bottom of the elevator car as shown in the diagram. Except for a braking system (not shown in the diagram), no other machinery is included in the elevator system.

Assuming that the fully loaded elevator car weighs 10,000 Newtons (roughly one ton), what is the maximum height to which the elevator can rise?

(a)   94.8 m
(b)   900.0 m
(c)   8.4 m


QUESTION 8*

After the design is unveiled at a stockholders’ meeting, Nillog Lifts’ Board of Directors orders the CEO to fire the company’s chief engineer. Why?

(a)   The elevator can ascend but never descend.
(b)   The action of the electric charges might be cancelled by the Earth’s magnetic field, causing the elevator to fall uncontrollably.


QUESTION 9**

This and the next three questions both refer to the circuit diagram and graphs shown below.

Initially the capacitors C1 and C2 are uncharged and switch S is open. At time t = 0 the switch is closed and capacitors begin charging. At what time t does the voltage difference between points A and B reach 90% of the battery voltage E? (Recall that 1 ms is 0.001 seconds.)

(a)   3.06 ms
(b)   7.68 ms
(c)   15.4 ms
(d)   17.2 ms
(e)   37.6 ms


QUESTION 10*

What is the maximum value of the current I that flows after the switch is closed?

(a)   1.2 mA
(b)   10 mA
(c)   15 mA


QUESTION 11***

After a very long time has passed, what is the voltage across capacitor C1?

(a)   0 V
(b)   4 V
(c)   8 V


QUESTION 12**

What is the charge on the top plate of capacitor C1 a very long time after the switch is closed?

(a)   12 μC
(b)   10 μC
(c)   8 μC


QUESTION 13*

A square, parallel plate capacitor has side length 1 m and separation 1 μm between its plates. What is its capacitance?

(a)   8.85 μF
(b)   1 μF
(c)   8.85 mF


QUESTION 14*

Charges are positioned as shown in this diagram. Assume that the +2 μC and -1 μC charges are held fixed. Calculate the horizontal component of the electric force on the -3 μC charge. Note that the gridlines drawn on the figure are spaced at 1 m intervals.

(a)   -6.75 × 10-3 N
(b)   -2.36 × 10-3 N
(c)   0 N
(d)   +4.51 × 10-3 N
(e)   +9.44 × 10-3 N


QUESTION 15*

Charges are positioned as shown in the following diagram. Assume that the +2 μC and -1 μC charges are held fixed. Calculate the energy required to remove the -3 μC charge to infinity.

(a)   7.02 × 10-3 J
(b)   5.00 × 10-3 J
(c)   8.41 × 10-3 J


QUESTION 16**

Positive and negative charges spaced at 1 m intervals are placed on the x axis as shown in the diagram. Calculate the work done to assemble this system assuming that the charges were very widely separated before being brought to their final positions.

(a)   0.068 J
(b)   0.032 J
(c)   0 J
(d)   -0.014 J
(e)   -0.021 J


QUESTION 17*

What is the resistance of an Aluminum wire which is 100 μm in diameter and 30 m long? The resistivity of Aluminum is ρ = 0.025 μΩ m.

(a)   25 Ω
(b)   40 Ω
(c)   55.5 Ω
(d)   95.5 Ω
(e)   300 Ω


QUESTION 18***

This and the next question pertain to the following situation:

The capacitors are initially uncharged. At time t = 0 the switch is closed. Which of the graphs below best represents the voltage difference between points A and B (VA-VB) as a function of time?

(a)   graph a
(b)   graph b
(c)   graph c


QUESTION 19**

During the charging process (after the switch is closed), the maximum currents flowing through R1 and R2 are equal.

(T)   True
(F)   False


QUESTION 20*

A square, parallel plate capacitor with capacitance 10 μF has side length L and separation 1 μm between its plates. The capacitor is filled with barium titanate (dielectric constant κ = 6000). What is L for this capacitor?

(a)   2.00 × 10-4 m
(b)   1.78 × 10-3 m
(c)   1.37 × 10-2 m
(d)   4.63 × 10-2 m
(e)   7.85 × 10-1 m


QUESTION 21*

Assuming that C1 = C2 = C3 = C4 = 1μF in the following diagram, what is the effective capacitance between points A and B?

(a)   0.2 μF
(b)   0.4 μF
(c)   0.5 μF
(d)   0.8 μF
(e)   1 μF


QUESTION 22*

What is wrong with this (incorrect) electric field line diagram for a pair of +2 μC charges?

(a)   All electric field lines must leave one of the charges and arrive at the other charge.

(b)   The diagram indicates that the electric field becomes increasingly strong with increasing distance along the y axis, contrary to the behavior expected from Coulomb’s law.

(c)   Since field lines indicate the direction of force exerted on a positive charge, pairs of field lines must cross through each other along the y axis.


QUESTION 23*

In this circuit C1 = C2 = 100 μF. Both capacitors were initially uncharged before the circuit was assembled. The battery voltage is V = 12 V. How much charge is now on the left plate of capacitor C1?

(a)   200 μC
(b)   400 μC
(c)   600 μC


QUESTION 24*

This and the next question pertain to the following situation:

In this circuit V = 12 V and C1 = C2 = 1 μF. How much energy is stored in capacitor C2?

(a)   12 μJ
(b)   36 μJ
(c)   72 μJ


QUESTION 25*

The air gaps in both capacitors are now filled with vulcanized rubber (κ = 3). How much does the charge on C1 increase after the rubber is inserted?

(a)   It does not increase.
(b)   It increases by a factor of 1.732 .
(c)   It increases by a factor of 3 .
(d)   It increases by a factor of 9 .
(e)   It increases by a factor of 27 .


QUESTION 26*

Charges are positioned as shown in this diagram. Assume that the +2 μC and -1 μC charges are held fixed. The energy required to remove the -3 μC charge from its indicated location to the point (x,y) = (1,1) is

(a)   minimized if the charge is moved along a single straight line from (2,2) to (1,1).

(b)   maximized if the charge is moved very far away, traveling parallel to the x axis, then moved directly to its final position at (1,1).

(c)   independent of the path taken to travel from (2,2) to (1,1).