25 Multiple-choice : Alternating current and EM waves.

(See attached file for full problem description)

---
1. The current in a certain ac circuit is independent of the frequency at a given voltage. Which combination of elements is most likely to comprise the circuit?

a. Resistors only
b. Inductors only
c. Capacitors only
d. A combination of inductors and resistors
e. A combination of inductors and capacitors

2. What is the capacitive reactance of a circuit comprised of a 65.0-μF capacitor and a 50.0-Hz generator?

a. 49.0Ω
b. 72.5Ω
c. 97.6Ω
d. 145Ω
e. 308Ω

3. When the frequency of an ac circuit is decreased, the current in the circuit increases. Which combination of elements is most likely to comprise the circuit?

a. Resistors only
b. Inductors only
c. Capacitors only
d. Capacitors and resistors
e. Inductors and capacitors

4. An ac voltage source that has a frequency f is connected across the ends of an inductor. Which one of the following statements correctly indicates the effect on the inductive reactance when the frequency is increases to 2f?

a. The inductive reactance increases by a factor of two.
b. The inductive reactance increases by a factor of four.
c. The inductive reactance is unchanged.
d. The inductive reactance decreases by a factor of four.
e. The inductive reactance decreases by a factor of two.

5. When the frequency of an ac circuit is increased at constant voltage, the current increases and then decreases. Which combination of elements is most likely to comprise this circuit?

a. Resistors only
b. Inductors only
c. Capacitors only
d. A combination of inductors and resistors
e. A combination of inductors and capacitors

6. An ac generator supplies an rms (not peak) voltage of 180 V at 60.0 Hz. Determine the peak voltage of the generator.

a. 180 V
b. 255 V
c. 300 V
d. 360 V
e. 480 V

7. The graph shows the impedance as a function of frequency for a series LCR circuit. At what frequency does the capacitor make the largest contribution?

a. f1
b. f2
c. f3
d. f1 or f3
e. f1 or f2 or f3

8. Which one of the following statements best explains why semiconductors in transistors are doped?

a. Doping makes the charge carriers mobile.
b. Doping makes the charge carriers immobile
c. Doping makes the semi-conducting materials non-conducting
d. Doing changes the conductive properties of the semiconductors.
e. Doping converts the semi-conducting materials into a metallic material like copper.

9. Which one of the following statements concerning diodes is false?

a. A diode is fabricated by forming junctions between one n-type and two p-type semiconductors or one p-type and two n-type semiconductors.
b. At an n-p junction in a diode that is not connected to a battery, an electric field exists across the junction.
c. A battery can be connected to a diode so that a continual flow of charge results.
d. A diode connected to an ac source allows current to flow only in one direction.
e. Holes move in a diode under a forward-bias condition.

10. A television station broadcasts at a frequency of 86 MHz. The circuit contains an inductor with an inductance L = 1.2 × 10-6 H and a variable-capacitance C. Determine the value of C that allows this television station to be tuned in.

a. 2.9 × 10-12 F
b. 5.8 × 10-12 F
c. 1.8 × 10-11 F
d. 3.6 × 10-11 F
e. 1.1 × 10-10 F

11. Complete the following sentence: The various colors of visible light differ in

a. Frequency only
b. Wavelength only
c. Their speeds in a vacuum
d. Frequency and wavelength
e. Frequency and their speed in a vacuum

12. When a radio telescope observes a region of space between two stars, it detects electromagnetic radiation that has a wavelength of 0.21 m. This radiation was emitted by hydrogen atoms in the gas and dust located in that region. What is the frequency of this radiation?

a. 7.1 × 1010 Hz
b. 2.1 × 1014 Hz
c. 3.0 × 108 Hz
d. 6.9 × 1011 Hz
e. 1.4 × 109 Hz

13. The average distance between the surface of the earth and the surface of the sun is 1.49 × 1011 m. How much time, in minutes, does it take for light leaving the surface of the sun to reach the earth?

a. Zero minutes
b. 2.9 × 10-3 minutes
c. 8.3 minutes
d. 74 minutes
e. 500 minutes

14. An electromagnetic wave has an electric field with peak value 250 N/C. What is the average intensity of the wave?

a. 0.66 W/m2
b. 0.89 W/m2
c. 83 W/m2
d. 120 W/m2
e. 170 W/m2

15. An astronomer observes electromagnetic waves emitted by oxygen atoms in a distant galaxy that have a frequency of 5.710 × 1014 Hz. In the laboratory on earth, oxygen atoms emit waves that have a frequency of 5.841 × 1014 Hz. Determine the relative velocity of the galaxy with respect to the astronomer on the earth. Note: The speed of light is 2.9979 × 108 m/s.

a. 6.724 × 106 m/s, away from earth
b. 6.724 × 106 m/s, toward earth
c. 2.931 × 108 m/s, away from earth
d. 4.369 × 104 m/s, toward earth
e. 4.369 × 104 m/s, away from earth

16. Unpolarized light of intensity So passes through two sheets of polarizing material whose transmission axes make an angle of 60° with each other as shown in the figure. What is the intensity of the transmitted beam, St?

a. So/4
b. So/8
c. 3So/4
d. So/16
e. Zero

17. Two polarizing sheets have their transmission axes parallel so that the intensity of unpolarized light transmitted through both of them is a maximum. Through what angle must either sheet be rotated if the transmitted intensity is 25% of the incident intensity?

a. 15°
b. 30°
c. 45°
d. 60°
e. 75°

18. Which one of the following statements provides the most convincing evidence that visible light is a form of electromagnetic radiation?

a. Two light sources can be coherent
b. Light can be reflected from a surface
c. Light can be diffracted through an aperture
d. Light can form a double-slit interference pattern
e. Light travels through vacuum at the same speed as X-rays.

19. Two slits are separated by 2.00 × 10-5 m. They are illuminated by light of wavelength 5.60 × 10-7 m. If the distance from the slits to the screen is 6.00 m, what is the separation between the central bright fringe and the third dark fringe?

a. 0.421 m
b. 0.224 m
c. 0.168 m
d. 0.084 m
e. 0.070 m

20. What is the minimum (non-zero) thickness of a benzene (n = 1.501) thin film that will result in constructive interference when viewed at normal incidence and illuminated with orange light (λvacuum = 615 nm)? A glass slide (ng = 1.620) supports the thin film.

a. 51.0 nm
b. 306 nm
c. 204 nm
d. 102 nm
e. 76.0 nm

21. A Michelson interferometer is used to measure the wavelength of light emitted from a monochromatic source. As the adjustable mirror is slowly moved through a distance DA = 0.0265 mm, an observer counts 411 alternations between bright and dark fields. What is the wavelength of the monochromatic light used in this experiment?

a. 193 nm
b. 227 nm
c. 258 nm
d. 346 nm
e. 369 nm

22. Light of wavelength 700.0 nm passes through a diffraction grating. The m = 0 and m = 1 bright spots are 6.0 cm apart on a screen positioned 2.0 cm from the grating. What is the spacing between the slits in the grating?

a. 233 nm
b. 423 nm
c. 467 nm
d. 738 nm
e. 1240 nm

23. Two stars are just barely resolved by a telescope with a lens diameter of 0.500 m. Determine the angular separation of the two stars. Assume incident light of wavelength 500.0 nm.

a. 1.22 × 10-6 rad
b. 5.66 × 10-5 rad
c. 2.44 × 10-7 rad
d. 4.88 × 10-5 rad
e. 1.22 × 10-7 rad

24. A 30.0-mm wide diffraction grating produces a deviation of 30.0° in the second order principal maxima. The wavelength of light is 600.0 nm. What is the total number of slits on the grating?

a. 10 000
b. 11 500
c. 12 500
d. 14 000
e. 15 000

25. Red light of wavelength 600.0 nm is incident on a grating. If the separation between the slits is 5.0 × 10-5 m, at what angle does the first principal maximum occur?

a. 0.6 × 10-2 rad
b. 0.8 × 10-2 rad
c. 1.2 × 10-2 rad
d. 3.6 × 10-2 rad
e. 5.0 × 10-2 rad