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 109. The exam period was 90 minutes; the average score was 70.5; the median score was 71. Click here to see page1 page2 of the formula sheet that came with the exam.

Consider the following arrangement of 4 polarizers. The first has a horizontal transmission axis, the second is oriented at 30° with respect to the horizontal, the third at 60° to the horizontal, and the fourth at 90° to the horizontal. The light incident on the first polarizer from the left is unpolarized.

The ratio of the final intensity of the transmitted light to the intensity of the incident light is:

(a) 0.65 (b) 0.32 (c) 0.2

(a) increase. (b) remain the same. (c) decrease.

(a) larger by a factor of 2. (b) smaller by a factor of 1/2. (c) larger by a factor of 1/cos^{2}30°. (d) smaller by a factor of cos^{2}30°. (e) the same as in the original situation.

(a) right circularly polarized. (b) left circularly polarized.

(a) (b) (c)

A laser sends a beam of light from water toward a plastic slab at the surface of the water. Above the plastic slab there is air.

What is the maximum value of the angle θ that the laser beam can make with the vertical and still have the beam of light emerge into the air above the plastic?

(a) 41.81° (b) 48.75° (c) 60.07°

(a) 2.73 × 10^{-10} s (b) 3.27 × 10^{-10} s (c) 4.49 × 10^{-10} s (d) 4.73 × 10^{-10} s (e) 5.97 × 10^{-10} s

(a) 63.3 μH (b) 126.7 μH (c) 190.0 μH (d) 253.3 μH (e) 316.6 μH

A typical electric guitar pickup consists of a coil of several thousand turns of very thin, enamel-coated copper wire wound around a fiber bobbin holding 6 rod-shaped permanent magnets. The figure below shows the 3 (neck, middle, bridge) pickups from a vintage 1959 Fender 'Stratocaster' guitar. A simplified model of an electric guitar pickup is the so-called RLC 'tank' circuit - as shown in the circuit diagram below on the right. The '59 Strat pickup coil has an inductance L = 2.6 H, in series with a resistance R = 5.5 KΩ, and a small capacitance C = 10^{-10} F in parallel with L and R, as shown. The electric guitar pickups are mounted in proximity to the 6 strings of the electric guitar, magnetizing them. When a magnetized guitar string vibrates, the magnetic flux Φ_{m} in the pickup coil varies in time with the string vibrations, inducing a small EMF, V(t), in the electric guitar pickup, which is then amplified in a guitar amplifier to produce an audible sound at the frequency of vibration of the guitar string!

The impedances, Z(ω), of the electric guitar pickup at ω = 0 and at ω = ∞ are:

(a) Z(ω=0) = 0 ohms and Z(ω=∞) = 0 ohms (b) Z(ω=0) = 0 ohms and Z(ω=∞) = R ohms (c) Z(ω=0) = R ohms and Z(ω=∞) = 0 ohms

(a) f_{o} = 9.9 × 10^{3} Hz (b) f_{o} = 6.2 × 10^{4} Hz (c) f_{o} = 7.1 × 10^{4} Hz

This question and the next two refer to this situation:

A series RLC circuit is shown in the figure on the right The resistance R = 200 Ω, inductance L = 2 H and capacitance C = 2 μF.

The instantaneous voltage, V(t), of the sine-wave generator and instantaneous current, I(t), flowing through the RLC circuit are 90° out of phase with each other at the resonant frequency, f_{o}, of the series RLC circuit.

(T) True (F) False

The voltage amplitude V_{C} across the capacitor at the resonant frequency, f_{o}, of the series RLC circuit is:

(a) 100 V (b) 500 V (c) 1000 V

(a) 0.0 J (b) 0.35 J (c) 0.50 J (d) 0.71 J (e) 1.00 J

A sinusoidally-varying voltage V(t) = V_{o}sinωt with amplitude V_{o} = 10 V and frequency of f = ω/(2π) = 100 Hz is impressed across the plates of a circular-shaped parallel plate air-gap capacitor of radius a = 1.0 cm and plate separation d= 0.01 mm. The amplitude of Maxwell's displacement current I_{D} flowing across the gap between the plates of this capacitor is:

(a) 0.28 × 10^{-6} A (b) 1.75 × 10^{-6} A (c) 3.50 × 10^{-6} A (d) 6.30 × 10^{-6} A (e) 9.45 × 10^{-6} A

(a) decrease by a factor of four. (b) decrease by a factor of two. (c) remain the same. (d) increase by a factor of two. (e) increase by a factor of four.

A plane electromagnetic wave is propagating in free space. The instantaneous electric field vector is given by E(r,t) = E_{o}cos(kz+ωt)x. The electric field amplitude associated with this plane wave is E_{o} = 100 V/m.

The corresponding instantaneous magnetic field vector is given by:

(a) B(r,t) = B_{o}cos(kz+ωt) x (b) B(r,t) = -B_{o}sin(kz+ωt) x (c) B(r,t) = -B_{o}cos(kz+ωt) y (d) B(r,t) = B_{o}sin(kz+ωt) y (e) B(r,t) = -B_{o}sin(kz+ωt) z

(a) 8.85 × 10^{-12} T (b) 3.33 × 10^{-7} T (c) 100 T

(a) 6.6 watts/m^{2} (b) 13.3 watts/m^{2} (c) 26.6 watts/m^{2}

(a) U_{A} = ¼ U_{B} (b) U_{A} = ½ U_{B} (c) U_{A} = U_{B} (d) U_{A} = 2 U_{B} (e) U_{A} = 4 U_{B}

In the circuit below, V = 6 volts, R = 10 ohms, L = 100 mH. The switch has been open for a long time. Then, at time t = 0, the switch is closed.

What is the current I_{∞} through L for t → ∞ ?

(a) 0.0 A (b) 0.3 A (c) 0.6 A

(a) R / L (b) R / (2L) (c) L / R (d) 2L / R (e) L / (2R)

Calculate the impedance, Z, of the circuit.

(a) 7.48 Ω (b) 10.14 Ω (c) 15.24 Ω (d) 22.42 Ω (e) 32.24 Ω

(a) V_{AC} and V_{R} are in phase. (b) V_{AC} leads V_{R}. (c) V_{AC} lags V_{R}.

(a) 0.005 A (b) 0.100 A (c) 0.500 A (d) 1.000 A (e) 4.000 A

(a) V_{C}(t_{1}) > V_{R}(t_{1}) > V_{L}(t_{1}) (b) V_{C}(t_{1}) > V_{L}(t_{1}) > V_{R}(t_{1}) (c) V_{R}(t_{1}) > V_{C}(t_{1}) > V_{L}(t_{1}) (d) V_{R}(t_{1}) > V_{L}(t_{1}) > V_{C}(t_{1}) (e) Cannot be determined from the information given.