*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 circuit, the impedance is determined by the resistance alone. Here's why:

1. **Correct Answer: Approximately equal to circuit resistance (D)**
   - At resonance, the inductive reactance ($X_L$) and capacitive reactance ($X_C$) are equal in magnitude but opposite in phase. This means they cancel each other out.
   - The formula for impedance ($Z$) in a series RLC circuit is:
     $$Z = R + j(X_L - X_C)$$
   - At resonance, $X_L = X_C$, so $X_L - X_C = 0$. Therefore, the impedance simplifies to:
     $$Z = R$$
   - Thus, the magnitude of the impedance is approximately equal to the circuit resistance.

2. **Why the other choices are incorrect:**
   - **Choice A: High, compared to the circuit resistance**
     - This is incorrect because at resonance, the impedance is not high; it is minimized to the resistance value.
   - **Choice B: Approximately equal to capacitive reactance**
     - This is incorrect because at resonance, the capacitive reactance is canceled out by the inductive reactance, leaving only the resistance.
   - **Choice C: Approximately equal to inductive reactance**
     - Similar to choice B, this is incorrect because the inductive reactance is canceled out by the capacitive reactance at resonance.

In summary, at resonance, the impedance of a series RLC circuit is purely resistive and equal to the circuit resistance.