Question E5D07:
What combines to create the self-resonance of a component?  

Choices:  
A: The component’s resistance and reactance  
B: The component’s nominal and parasitic reactance  
C: The component’s inductance and capacitance  
D: The component’s electrical length and impedance    

Correct Answer is  B: The component’s nominal and parasitic reactance  

To understand self-resonance, remember that real components are not ideal—they include unintended (parasitic) reactances that can cancel the intended (nominal) reactance at some frequency.

1) Why the correct answer is correct (B)
- Self-resonance occurs when a component’s intended reactance and its parasitic reactance are equal in magnitude and opposite in sign, so the total reactance goes to zero:
  $$X_{\text{total}}(f) = X_{\text{nom}}(f) + X_{\text{par}}(f) \approx 0$$
- Example for an inductor: its inductance L (nominal, +j) resonates with its distributed winding capacitance C_p (parasitic, −j):
  $$f_{\text{sr}} \approx \frac{1}{2\pi\sqrt{L C_p}}$$
- Example for a capacitor: its capacitance C (nominal, −j) resonates with its series lead inductance L_s (parasitic, +j):
  $$f_{\text{sr}} \approx \frac{1}{2\pi\sqrt{L_s C}}$$
- In both cases, the self-resonance is produced by the combination of nominal and parasitic reactances.

2) Why the other choices are incorrect
- A: The component’s resistance and reactance  
  Resistance does not create resonance; it dissipates energy and sets Q. Resonance requires cancellation of reactive terms (inductive vs. capacitive), not resistance.
- C: The component’s inductance and capacitance  
  Too generic as stated. Resonance within a single component is specifically due to the component’s nominal reactance interacting with its parasitic reactance (e.g., an inductor’s own parasitic capacitance). The exam answer emphasizes the nominal vs. parasitic pairing.
- D: The component’s electrical length and impedance  
  This applies to transmission lines and antennas, not lumped components like individual inductors or capacitors in the usual sense.

3) Useful formulas and rules of thumb
- Reactances:
  $$X_L = +2\pi f L,\quad X_C = -\frac{1}{2\pi f C}$$
- Resonance condition (magnitude equality):
  $$|X_L| = |X_C| \;\Rightarrow\; f_0 = \frac{1}{2\pi\sqrt{LC}}$$
- For self-resonance in real parts:
  - Inductor with parasitic capacitance C_p:
    $$f_{\text{sr}} \approx \frac{1}{2\pi\sqrt{L C_p}}$$
  - Capacitor with parasitic inductance L_s:
    $$f_{\text{sr}} \approx \frac{1}{2\pi\sqrt{L_s C}}$$
- Rule of thumb: Use components well below their self-resonant frequency (often at least a decade lower) if you want them to behave like ideal L or C. Resistance (ESR/series R) lowers Q and slightly shifts/broadens resonance but does not create it.