Chapter 9 Quiz — Phasors and Complex Impedance
Chapter 9 Quiz
1. A phasor is best described as:
A) A time-domain sinusoidal function B) A complex number representing the amplitude and phase of a sinusoid C) The derivative of a sinusoidal signal D) A rotating vector that varies with time
2. What is the impedance of a capacitor \(C\) at angular frequency \(\omega\)?
A) \(j\omega C\) B) \(\omega C\) C) \(\dfrac{1}{j\omega C}\) D) \(j\omega L\)
3. What is the impedance of an ideal inductor \(L\) at angular frequency \(\omega\)?
A) \(\dfrac{1}{j\omega L}\) B) \(j\omega L\) C) \(\omega L\) D) \(\dfrac{1}{\omega L}\)
4. A series RLC circuit has \(X_L > X_C\) at a given frequency. The circuit behaves:
A) Capacitively — current leads voltage B) Resistively — no phase shift C) Inductively — voltage leads current D) As if at resonance
5. In the impedance triangle, if resistance is \(R\) and net reactance is \(X\), what is \(|Z|\)?
A) \(R + X\) B) \(R/X\) C) \(R^2 + X^2\) D) \(\sqrt{R^2 + X^2}\)
6. What happens to capacitive reactance \(X_C\) as frequency increases?
A) Increases proportionally B) Remains constant C) Decreases D) Becomes negative
7. For a pure resistor in an AC circuit, the phase relationship between voltage and current is:
A) Voltage leads current by 90° B) Current leads voltage by 90° C) In phase (0°) D) Voltage leads by 45°
8. A 10 mH inductor operates at \(f = 5\) kHz. What is its inductive reactance \(X_L\)?
A) 50 Ω B) 314 Ω C) 628 Ω D) 3,142 Ω
9. Phasor analysis is valid when:
A) All sources are DC B) The circuit has only resistors C) All sources are sinusoidal at the same frequency in steady state D) The circuit is in a transient switching state
10. At series resonance, the total impedance of the RLC circuit equals:
A) Zero B) \(X_L\) C) \(R\) D) \(X_L + X_C\)
Answer Key
| Question | Answer | Brief Reason |
|---|---|---|
| 1 | B | A phasor is a static complex number encoding magnitude and phase — no time dependence |
| 2 | C | \(Z_C = 1/(j\omega C)\); purely imaginary, decreases with frequency |
| 3 | B | \(Z_L = j\omega L\); purely imaginary, increases with frequency |
| 4 | C | Net reactance \(X_L - X_C > 0\) → inductive → voltage leads current |
| 5 | D | Pythagorean theorem on the impedance triangle: ( |
| 6 | C | \(X_C = 1/(\omega C)\); as \(f\) rises, \(X_C\) falls — capacitors pass high frequencies |
| 7 | C | \(Z_R = R\) is purely real; no imaginary part → 0° phase shift |
| 8 | B | \(X_L = 2\pi fL = 2\pi \times 5000 \times 0.01 \approx 314\) Ω |
| 9 | C | Phasors require sinusoidal steady state at a single shared frequency |
| 10 | C | At resonance \(X_L = X_C\), they cancel; only \(R\) remains |