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

*Correct Answer is  D: Approximately equal to circuit resistance*  

### AI Response: (may contain errors)  

At resonance in a series RLC (Resistor, Inductor, Capacitor) circuit, the impedance behaves in a specific way. 

1. **Correct Answer Explanation (D: Approximately equal to circuit resistance)**:
   - At resonance, the inductive reactance ($X_L$) and capacitive reactance ($X_C$) are equal, which means they cancel each other out. This results in the total impedance ($Z$) of the circuit being primarily resistive.
   - The formula for impedance in a series RLC circuit is:
     $$Z = R + j(X_L - X_C)$$
   - At resonance, since $X_L = X_C$, the equation simplifies to:
     $$Z = R + j(0) = R$$
   - Therefore, the magnitude of the impedance is approximately equal to the circuit resistance.

2. **Why the Other Choices are Incorrect**:
   - **A: High, compared to the circuit resistance**: This is incorrect because at resonance, the impedance is not high; it is minimized to just the resistance.
   - **B: Approximately equal to capacitive reactance**: This is incorrect because at resonance, the capacitive reactance is canceled out by the inductive reactance, so it does not contribute to the impedance.
   - **C: Approximately equal to inductive reactance**: This is also incorrect for the same reason as choice B; at resonance, the inductive reactance is canceled out by the capacitive reactance.

3. **Useful Formulas and Rules of Thumb**:
   - The resonant frequency ($f_0$) of a series RLC circuit can be calculated using:
     $$f_0 = \frac{1}{2\pi\sqrt{LC}}$$
   - At resonance, the circuit behaves like a purely resistive circuit, and the impedance is simply the resistance $R$.

In summary, at resonance, the impedance of a series RLC circuit is approximately equal to the circuit resistance, making option D the correct choice.