Spring 2006 Physics 102 Hour Exam 2
(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 100. The exam period was 90 minutess; the mean score was 66.4; the median was 67. Click here to see page1 page2 of 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*

A rectangular coil of 12 turns has sides a = 0.2 m and b = 0.1 m. The coil rotates about the y axis with angular velocity ω = 20 rad/s in a uniform magnetic field Bx = 0.05 T (By = Bz = 0). A resistor is connected in series with the coil as shown in the diagram.

What is the maximum voltage produced across the resistor by the coil?

(a)   20 mV
(b)   50 mV
(c)   240 mV


QUESTION 2*

A laboratory power source supplies a voltage

V(t) = 480 sin(ωt)
to an experiment.

(a)   480 V
(b)   339.4 V
(c)   240 V


QUESTION 3*

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

A solenoid of length 0.5 m and radius .03 m is wound with 1000 turns.

What is the inductance of this solenoid?

(a)   7.1 mH
(b)   3.55 mH
(c)   14.2 μH


QUESTION 4*

The solenoid is connected to a power supply that provides the solenoid with 1.5 A of current. What is the magnetic field inside the solenoid?

(a)   1.88 mT
(b)   2.5 mT
(c)   3.77 mT


QUESTION 5*

The solenoid is now stretched so that it is 1 m long but still wound with 1000 turns. Its diameter is unchanged. Relative to the original length solenoid, the newly stretched solenoidís inductance has

(a)   decreased.
(b)   increased.
(c)   not changed.


QUESTION 6*

This and the next question pertain to the following situation.

The phasor diagram at the left corresponds to a series RCL circuit driven by a sine wave generator with maximum voltage of 30 V. The magnitudes of R, XL and XC are labeled on the phasor diagram.

What is the magnitude of the total impedance Z of the circuit?

(a)   190 Ω
(b)   50 Ω
(c)   70 Ω


QUESTION 7**

What is the maximum voltage across the resistor in this circuit?

(a)   18 V
(b)   30 V
(c)   15 V
(d)   25 V
(e)   10 V


QUESTION 8*

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

The phase angle Φ describes the phase relationship between the voltage supplied by the signal generator, V(t) = Vmaxsin(2πft + Φ), and the current that flows in the circuit, I(t) = Imaxsin(2πft). What is the phase angle at frequency f = 600 Hz ?

(a)   56.9° (= 0.993 radians)
(b)   -56.9° (= -0.993 radians)
(c)   27° (= 0.471 radians)
(d)   -27° (= -0.471 radians)
(e)   35.5° (= 0.620 radians)


QUESTION 9***

In a different RLC circuit the generator provides a voltage V(t) = 120 sin(2π60t) so that the current in the circuit is I(t) = 5 sin(2π60t +Φ). The phase angle Φ is 25° (0.436 radians). What is the maximum power dissipated in this circuit?

(a)   600 W
(b)   543.8 W
(c)   300 W


QUESTION 10**

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

A conducting metal band containing a 5 Ω resistor is formed into a circle of radius R as shown in the diagram. The band runs through a computer-controlled motorized screw-drive so that the circumference of the band changes as the screw-drive turns, changing the size of the circle smoothly as dictated by the computer. The circle always lies in the plane of the paper, perpendicular to a uniform magnetic field B of 0.25 T.

The computer-controlled screw drive turns so as to decrease the circumference of the loop. Because of this,

(a)   a current that flows clockwise is induced in the loop.
(b)   a current that flows counterclockwise is induced in the loop.


QUESTION 11**

The computer is now programmed so that area A of the loop decreases at a constant rate: A(t) = (1 - 0.2t) m2. The magnitude of the current induced in the loop during the time interval from t = 2 to t = 2.1 is:

(a)   50 mA
(b)   35 mA
(c)   10 mA
(d)   5 mA
(e)   1 mA


QUESTION 12***

The computer that regulates the size of the loop now causes the screw-drive to set the area of the loop to A(t) = (1 + 0.5sin(πt)) m2 as shown in the following graph.

The magnitude of the current induced in the loop is greatest at which of the following times?

(a)   t = 0.5
(b)   t = 1.0
(c)   t = 1.5


QUESTION 13*

This and the next question pertain to the following situation.

A transformer with a 100-turn primary coil and 300-turn secondary coil is wired to a signal generator and 50 Ω resistor as shown in the following diagram. The signal generator produces a 60 Hz sine wave.

The signal generator's peak voltage is 24 volts. How much peak power is delivered to the resistor attached to the transformer's secondary?

(a)   11.52 W
(b)   72 W
(c)   103.68 W
(d)   1200 W
(e)   15000 W


QUESTION 14**

The ratio of the power supplied by the signal generator to the power delivered to the resistor is

(a)   Psignal generator / Presistor = 0.25
(b)   Psignal generator / Presistor = 1
(c)   Psignal generator / Presistor = 4


QUESTION 15*

This and the next question pertain to the following situation.

A generator is built by winding 30 turns around a circular form of radius 0.1 m and then attaching it to a horizontal motor-driven shaft as shown in the figure below. The loop rotates in a uniform vertical magnetic field of strength B = 0.3 T; the wire of the loop is somewhat resistive so that the total resistance of the 30 loops is 4 Ω. The angle Φ between the normal to the loop and the magnetic field obeys the equation Φ = 75t radians. (This means that ω = 2πf = 75 radians/second.)

At the time t shown in the diagram, Φ = π/2 radians = 90°.

When the orientation of the loop is as shown in the figure, the flux of magnetic field through the loop is at its maximum value.

(T)   True
(F)   False


QUESTION 16**

When the orientation of the loop is as shown in the figure, the induced current in the loop is at its maximum value.

(T)   True
(F)   False


QUESTION 17**

The late 16th century artist El Greco (Domenikos Theotokopoulos) painted A View of Toledo roughly 300 years before the Spanish city briefly adopted 110 V, 50 Hz AC power as its standard.

An American traveller with an electric razor enters a hardware store in Toledo hoping to buy a transformer to convert 110 V, 50 Hz power into U.S. standard 110 V, 60 Hz power. He describes his problem to the proprietor and asks for help. The owner of the hardware store explains that he should buy

(a)   a transformer whose primary has 1.2 times as many windings as its secondary.
(b)   a transformer whose secondary has 1.2 times as many windings as its primary.
(c)   razor blades and shaving cream since transformers convert voltage, but not frequency


QUESTION 18*

This and the next question pertain to this series RLC circuit:

You are trying to make isotopically pure Uranium235 to sell on the black market. You have a mixture of U235 and U238 which you are trying to separate by ionizing it and passing it through a region with uniform 1.5 T magnetic field, after which the ions strike a screen. The masses of the two isotopes are M238 = 3.95 × 10-25 kg and M235 = 3.90 × 10-25 kg. The ions are all singly ionized so they have charge q235 = q238 = +1.6 × 10-19 C. All ions have the same velocity, as shown, of v = 100 m/s. The magnetic field is into the page.

Which of the two isotopes strikes higher on the screen?

(a)   U235
(b)   U238


QUESTION 19**

How large a B field would be required to separate the two isotopes by 1 mm on the screen? (Note that the ions travel through semicircular paths before striking the screen so that the distance from entrance to their impact points on the screen are twice the radii of their trajectories.)

(a)   60.25 T
(b)   6.25 T
(c)   0.625 T
(d)   0.0625 T
(e)   0.00625 T


QUESTION 20**

A wire carrying current I1 is resting next to a loop with 2 turns of radius R carrying current I2. The directions of the currents are as shown. At what value of the ratio I1 / I2 does the field at the center of the circle vanish?

(a)   π / 2
(b)   2 π
(c)   1 / 2


QUESTION 21**

This and the next question pertain to the following situation.

A particle of charge q = -3 μC is traveling with speed v = 50 m/s in a uniform field B = 4 T, as shown. θ = 22.5°.

What is the force on the particle?

(a)   55.4 μN out of the page
(b)   230 μN into the page
(c)   230 μN out of the page
(d)   554 μN into the page
(e)   23.0 μN into the page


QUESTION 22***

The trajectory of the particle is best described as

(a)   a helix.
(b)   a circle oriented in the plane of the page.
(c)   a circle oriented perpendicular to the page.


QUESTION 23**

This and the next question pertain to the following situation.

A square, horizontal loop with side length L = 0.1 m is attached to a pivot around which it may freely rotate. A magnetic field B = 0.5 T is applied parallel to the plane of the loop, as shown. A battery (not shown) forces a constant current to flow around the loop.

Because of the torque exerted by the magnetic field, the loop would begin to rotate were it not for a mass m = 1 kg suspended from one side of the loop. Recall that g = 9.8 m/s2. †

Which way must the current flow in the loop to keep it from rotating due to the weight of the mass?

(a)   as indicated by the arrow marked "A"
(b)   as indicated by the arrow marked "B"


QUESTION 24***

How large would the current have to be?

(a)   196 A
(b)   98 A
(c)   49 A
(d)   24.5 A
(e)   12.25 A


QUESTION 25*

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

A two-loop circuit is attached to a rotating pivot and suspended in a uniform magnetic field, B, pointing to the right. R = 1 Ω, V = 10 V, B = 1 T , and L = 1 m.

Initially the switch S is closed. In which direction will the loop turn? (Refer to the arrows drawn around the pivot.)

(a)   as indicated by arrow A
(b)   as indicated by arrow B
(c)   The loop will not turn.


QUESTION 26**

The switch S is opened so that current only flows in the left loop. What is the torque on the loop?

(a)   0.1 N-m
(b)   0.5 N-m
(c)   1 N-m
(d)   5 N-m
(e)   10 N-m


QUESTION 27**

Which way will the loop turn after switch S is opened?

(a)   as indicated by arrow A
(b)   as indicated by arrow B
(c)   The loop will not turn.