Review the following concepts if needed:

- Alternating Current Help
- Phase Angle Help
- Inductive Reactance Formula Help
- Capacitive Reactance Help

**Waves and Phases Test**

A good score is eight correct.

1. Suppose the current lags the voltage in a circuit by 45° of phase. The circuit contains 10 ohms of inductive reactance. How much resistance does the circuit contain? Express the answer to two significant figures.

(a) 5.0 ohms

(b) 10 ohms

(c) 89 ohms

(d) This question makes no sense because the reactance is capacitive, not inductive

2. Suppose the angular frequency of a wave is specified as 3.14159 × 10 ^{6} rad/s. What is the period of this wave in seconds? Express the answer to three significant figures.

(a) 1.59 × 10 ^{–7}

(b) 3.18 × 10 ^{–7}

(c) 2.00 × 10 ^{–6}

(d) 1.00 × 10 ^{–6}

3. Approximately how many radians are in a quarter of an AC cycle?

(a) 0.7854

(b) 1.571

(c) 3.142

(d) 6.284

4. Find the extent to which the current leads the voltage in an AC electronic circuit that has 775 ohms of resistance and 775 ohms of capacitive reactance. Express your answer in degrees to three significant figures.

(a) 88.7°

(b) 57.3°

(c) 45.0°

(d) None of the above

5. In the stronger wave illustrated by Fig. 9-12, what fraction of a cycle, in degrees, is represented by one horizontal division?

(a) 60°

(b) 90°

(c) 120°

(d) This question cannot be answered as stated

6. What is the difference in phase between the stronger and weaker waves illustrated in Fig. 9-12?

(a) 30°

(b) 45°

(c) 60°

(d) This question cannot be answered as stated

7. The peak voltage that appears at a common household utility outlet in the United States is approximately +160 volts. What is the instantaneous voltage three-quarters of the way into a cycle, based on this figure for the peak voltage?

(a) +40.0 volts

(b) –61.2 volts

(c) +113 volts

(d) –160 volts

8. Suppose there are two sine waves *X* and *Y* having identical frequency. Suppose that in a vector diagram, the vector for wave *x* is 10° counter-clockwise from the vector representing wave *Y.* This means that

(a) wave *X* leads wave *Y* by 10°

(b) wave *X* leads wave *Y* by 170°

(c) wave *X* lags wave *Y* by 10°

(d) wave *X* lags wave *Y* by 170°

9. Suppose there are two sine waves having identical frequency, and their vector representations are at right angles to each other. What is the difference in phase?

(a) More information is needed to answer this question

(b) 90°

(c) 180°

(d) 2π rad

10. If the angular frequency of a wave is 1000 Hz, then the period of the wave is

(a) 0.001000 second

(b) 0.00628 second

(c) 0.360 second

(d) impossible to determine because the angular frequency, as stated, makes no sense

**Answers:**

1. b

2. c

3. b

4. c

5. c

6. d

7. d

8. a

9. b

10. d

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