Question E5A03:
What is the magnitude of the impedance of a series RLC circuit at resonance?  

Choices:  
A: High, compared to the circuit resistance  
B: Approximately equal to capacitive reactance  
C: Approximately equal to inductive reactance  
D: Approximately equal to circuit resistance    

Correct Answer is  D: Approximately equal to circuit resistance  

At series resonance, the inductor and capacitor reactances cancel, leaving only resistance.

Key formulas:
- Series RLC impedance:
  $$Z = R + j\left(\omega L - \frac{1}{\omega C}\right)$$
- Resonant angular frequency:
  $$\omega_0 = \frac{1}{\sqrt{LC}}$$
- At resonance, since $X_L = \omega_0 L$ and $X_C = 1/(\omega_0 C)$, we have $X_L - X_C = 0$, so:
  $$Z(\omega_0) = R \quad \Rightarrow \quad |Z| = R$$

Why D is correct (Approximately equal to circuit resistance):
- At resonance, the net reactance is zero, so the impedance is purely resistive. Its magnitude equals the total series resistance (the explicit resistor plus any ESR of L and C).

Why the others are incorrect:
- A (High, compared to the circuit resistance): In a series RLC, impedance is minimum at resonance, not high; current is maximum and limited by R.
- B (Approximately equal to capacitive reactance): At resonance, the net reactance is zero; it is not equal to $X_C$.
- C (Approximately equal to inductive reactance): Same reason; not equal to $X_L$.

Rules of thumb:
- Series resonance: minimum impedance, $|Z| \approx R$; current peaks.
- Parallel resonance: maximum impedance; current from the source is minimized.