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 127. The exam period was 90 minutes; the average score was 99.6; the median score was 102. Click here to see page1 page2 of the formula sheet that came with the exam.

At what frequency, f (= ω/2π) is I_{rms} maximum?

(a) 0 Hz (b) 3.55 × 10^{-5} Hz (c) 712 Hz (d) 4.47 × 10^{3} Hz (e) 3.18 × 10^{6} Hz

(a) leads (b) lags (c) is in phase with

(T) True (F) False

What is the maximum current in the circuit?

(a) I_{MAX} = 1.00 A (b) I_{MAX} = 0.71 A (c) I_{MAX} = 0.50 A (d) I_{MAX} = 0.35 A (e) I_{MAX} = 0.25 A

Is the angular frequency ω greater than, less than, or equal to ω_{o}, the resonant frequency?

(a) ω > ω_{o} (b) ω < ω_{o} (c) ω = ω_{o}

An AC voltage source with angular frequency ω = 100 rad/s and root-mean-square voltage E_{rms} = 110 V drives an RLC circuit.

What is the RMS current flowing in the circuit?

(a) I_{rms} = 0.8 A (b) I_{rms} = 1.9 A (c) I_{rms} = 2.7 A (d) I_{rms} = 8.2 A (e) I_{rms} = 11.0 A

(a) I_{rms} will decrease. (b) I_{rms} will remain the same. (c) I_{rms} will increase.

What is the peak power that the generator delivers during each cycle?

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

(a) B = 8.10 × 10^{-6} T (b) B = 1.42 × 10^{-5} T (c) B = 2.55 × 10^{-5} T

Unpolarized light travels along the positive z-axis and passes through two ideal, linear polarizers with transmission axes (TA) shown as arrows in the below figure. The TA of the first polarizer is inclined at an angle Φ with respect to the x-axis, while the TA of the second polarizer is aligned along the y-axis. In Region #1 (before striking the 1^{st} linear polarizer), the intensity is I_{1}. In Region #2 (between the 1^{st} and 2^{nd} linear polarizer) the intensity is I_{2}. In Region #3 (after the 2^{nd} linear polarizer) the intensity is I_{3}. The electric field in Region #2 is given by:

E = 0.8 E_{2} x cos (kz-ωt) + 0.6 E_{2} y cos (kz-ωt)

Find the intensity ratio I_{2} / I_{1}.

(a) I_{2} / I_{1} = 0.80 (b) I_{2} / I_{1} = 0.71 (c) I_{2} / I_{1} = 0.64 (d) I_{2} / I_{1} = 0.50 (e) I_{2} / I_{1} = 0.36

(a) I_{3} / I_{2} = 0.80 (b) I_{3} / I_{2} = 0.71 (c) I_{3} / I_{2} = 0.64 (d) I_{3} / I_{2} = 0.50 (e) I_{3} / I_{2} = 0.36

Light traveling in diamond is incident on a 3 cm thick piece of sapphire. It enters the sapphire at an angle of 50° as shown. When it reaches a third material, it undergoes total internal reflection.

What is the incident angle θ_{1} of the light in the diamond?

(a) θ_{1} = 24° (b) θ_{1} = 34° (c) θ_{1} = 44° (d) θ_{1} = 54° (e) θ_{1} = 64°

(a) x = 6.4 cm (b) x = 7.2 cm (c) x = 8.6 cm (d) x = 9.3 cm (e) x = 12.1 cm

(a) ice only (b) fluorite only (c) titanium dioxide (d) either ice or fluorite (e) none of the above

(a) θ = 12.5° (b) θ = 13.6° (c) θ = 15.2°

An electromagnetic plane wave is propagating in empty space. The electric field at time t = 0 over two wavelengths is sketched in the figure above. The E-field is given by E(x,y,z,t) = i E_{0} sin(kz+ωt). Here, i is the unit vector in the +x direction, j is the unit vector in the +y direction, and k is the unit vector in the +z direction.

Which one of the following expressions describes the magnetic field of this electromagnetic wave?

(a) B(x,y,z,t) = i B_{0} sin(kz+ωt) (b) B(x,y,z,t) = j B_{0} sin(kz+ωt) (c) B(x,y,z,t) = k B_{0} cos(kz+ωt) (d) B(x,y,z,t) = -j B_{0} sin(kz+ωt) (e) B(x,y,z,t) = -i B_{0} cos(kz+ωt)

(a) <u> = 0.67 × 10^{-9} J/m^{3} (b) <u> = 1.23 × 10^{-9} J/m^{3} (c) <u> = 1.90 × 10^{-9} J/m^{3} (d) <u> = 2.82 × 10^{-9} J/m^{3} (e) <u> = 3.33 × 10^{-9} J/m^{3}

(a) B_{o} = 7.28 × 10^{-9} tesla (b) B_{o} = 3.05 × 10^{-8} tesla (c) B_{o} = 7.58 × 10^{-8} tesla (d) B_{o} = 9.15 × 10^{-8} tesla (e) B_{o} = 1.53 × 10^{-7} tesla

(a) It would be one half its previous value. (b) It would be equal to its previous value. (c) It would be twice its previous value.

(a) B_{2} > B_{1} > B_{3} = 0 (b) B_{2} > B_{1} = B_{3} > 0 (c) B_{2} > B_{1} = B_{3} = 0

A parallel plate capacitor is charging with time. The current is flowing in the wires as shown in the figure. Point P lies a distance r from the wire to the left of the capacitor, and point Q lies between the capacitor plates the same distance r from the center of the capacitor. r is less that the radius of the capacitor plates. Let B_{P} be the magnetic field at point P and let B_{Q} and E_{Q} be the magnetic and electric fields at point Q.

While the capacitor is charging, which of the following statements is true?

(a) B_{P} ≠ 0, B_{Q} = 0, E_{Q} = 0 (b) B_{P} = 0, B_{Q} ≠ 0, E_{Q} = 0 (c) B_{P} = 0, B_{Q} ≠ 0, E_{Q} ≠ 0 (d) B_{P} ≠ 0, B_{Q} = 0, E_{Q} ≠ 0 (e) B_{P} ≠ 0, B_{Q} ≠ 0, E_{Q} ≠ 0

(a) | B_{P} | < | B_{Q} | (b) | B_{P} | = | B_{Q} | (c) | B_{P} | > | B_{Q} |

(a) B_{Q} = 0, E_{Q} = 0 (b) B_{Q} ≠ 0, E_{Q} = 0 (c) B_{Q} = 0, E_{Q} ≠ 0

The circuit shown below consists of a 9 V battery, three resistors, an ideal inductor and a switch. Assume that the switch has been open for a long time.

The switch is now closed at t = 0. Immediately afterwards, what is the current I_{3} flowing through resistor R_{3}?

(a) 10.2 mA (b) 25.0 mA (c) 34.6 mA (d) 50.0 mA (e) 150.0 mA

(a) 4.3 μsec (b) 10.6 μsec (c) 20.0 μsec (d) 34.8 μsec (e) 60.0 μsec