*Question E5A04:
What is the magnitude of the impedance of a parallel RLC circuit at resonance?*  

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

### AI Response: (may contain errors)  

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

1. **Correct Answer Explanation**:  
   - 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, resulting in the circuit behaving primarily like a resistor. Therefore, the total impedance ($Z$) of the circuit is approximately equal to the resistance ($R$) of the circuit.  
   - Mathematically, at resonance:  
   $$X_L = X_C$$  
   This leads to:  
   $$Z \approx R$$  

2. **Incorrect Choices Explanation**:  
   - **Choice B: Approximately equal to inductive reactance**: This is incorrect because at resonance, the inductive reactance is canceled out by the capacitive reactance, so the impedance is not equal to the inductive reactance.
   - **Choice C: Low compared to the circuit resistance**: This is incorrect because at resonance, the impedance is not low; it is approximately equal to the resistance, which is a higher value.
   - **Choice D: High compared to the circuit resistance**: This is also incorrect because the impedance at resonance is not high; it is approximately equal to the resistance, not exceeding it.

3. **Useful Formulas and Rules of Thumb**:  
   - The resonant frequency ($f_0$) for a parallel RLC circuit can be calculated using:  
   $$f_0 = \frac{1}{2\pi\sqrt{LC}}$$  
   where:
   - $L$ = inductance in henries
   - $C$ = capacitance in farads  
   - At resonance, the circuit's impedance is dominated by the resistance, making it a critical point for tuning and maximizing power transfer in RF applications. 

This understanding is crucial for the Extra Class exam and practical applications in amateur radio.