Chapter 8 Quiz — AC Signals and Sinusoidal Waveforms
Chapter 8 Quiz
1. In the expression \(v(t) = V_m \sin(\omega t + \phi)\), which parameter represents the peak amplitude?
A) \(\omega\) B) \(\phi\) C) \(V_m\) D) \(t\)
2. A sinusoidal voltage has a peak value of \(V_m = 170\) V. What is its RMS value?
A) 85 V B) 108 V C) 120 V D) 240 V
3. A sinusoidal signal has a frequency of \(f = 400\) Hz. What is its period \(T\)?
A) 400 s B) 0.4 ms C) 2.5 ms D) 25 ms
4. Given \(v_1(t) = V_m \sin(\omega t)\) and \(v_2(t) = V_m \sin(\omega t + 60°)\), which statement is correct?
A) \(v_1\) leads \(v_2\) by 60° B) \(v_2\) leads \(v_1\) by 60° C) The signals are in phase D) \(v_2\) lags \(v_1\) by 30°
5. What is the angular frequency \(\omega\) of the US power grid (60 Hz)?
A) 60 rad/s B) 120 rad/s C) \(120\pi\) rad/s D) \(60\pi\) rad/s
6. What is the full-cycle average value of a pure, unbiased sinusoidal waveform?
A) \(V_m/\sqrt{2}\) B) \(2V_m/\pi\) C) \(V_m\) D) Zero
7. Euler's formula states that \(e^{j\theta}\) equals:
A) \(\cos\theta - j\sin\theta\) B) \(j\cos\theta + \sin\theta\) C) \(\cos\theta + j\sin\theta\) D) \(\sin\theta + j\cos\theta\)
8. A signal that satisfies \(x(t) = x(t + T)\) for all \(t\) is called:
A) Aperiodic B) Transient C) Periodic D) Stochastic
9. A voltage signal is \(v(t) = 6 + 10\sin(377t)\) V. What is the RMS value of the AC component only?
A) 6 V B) 7.07 V C) 10 V D) 9.27 V
10. What is the crest factor of a pure sinusoid?
A) 1.0 B) \(\sqrt{2}\) C) 2.0 D) \(\pi/2\)
Answer Key
| Question | Answer | Brief Reason |
|---|---|---|
| 1 | C | \(V_m\) is the coefficient of the sine function — the peak value |
| 2 | C | \(V_{rms} = V_m/\sqrt{2} = 170/1.414 \approx 120\) V |
| 3 | C | \(T = 1/f = 1/400 = 2.5\) ms |
| 4 | B | A positive phase offset means \(v_2\) reaches its peak earlier — it leads |
| 5 | C | \(\omega = 2\pi f = 2\pi \times 60 = 120\pi \approx 377\) rad/s |
| 6 | D | Positive and negative half-cycles cancel; full-cycle average is zero |
| 7 | C | Euler's formula: \(e^{j\theta} = \cos\theta + j\sin\theta\) |
| 8 | C | This is the definition of a periodic signal |
| 9 | B | \(V_{AC,rms} = 10/\sqrt{2} = 7.07\) V |
| 10 | B | Crest factor \(= V_m / V_{rms} = V_m / (V_m/\sqrt{2}) = \sqrt{2}\) |