*Question E5A08:
What is the phase relationship between the current through and the voltage across a series resonant circuit at resonance?*  

*Correct Answer is  C: The voltage and current are in phase*  

### AI Response: (may contain errors)  

In a series resonant circuit, resonance occurs when the inductive reactance ($X_L$) and capacitive reactance ($X_C$) are equal, effectively canceling each other out. At this point, the circuit behaves purely resistively.

1. **Correct Answer Explanation (C):**  
   - At resonance, the impedance of the circuit is purely resistive, meaning there is no reactive component to cause a phase shift between voltage and current.
   - Therefore, the voltage and current are in phase, meaning they reach their maximum and minimum values simultaneously.

2. **Why Other Choices Are Incorrect:**
   - **Choice A (The voltage leads the current by 90 degrees):**  
     - This would occur in a purely inductive circuit, not in a resonant circuit at resonance.
   - **Choice B (The current leads the voltage by 90 degrees):**  
     - This would occur in a purely capacitive circuit, not in a resonant circuit at resonance.
   - **Choice D (The voltage and current are 180 degrees out of phase):**  
     - This would imply that the circuit is purely reactive, which is not the case at resonance.

3. **Useful Formulas and Rules of Thumb:**
   - At resonance:  
     $$X_L = X_C$$  
   - Impedance at resonance is purely resistive:  
     $$Z = R$$  
   - Phase angle ($\phi$) between voltage and current at resonance:  
     $$\phi = 0^\circ$$  

Understanding these concepts helps in recognizing that at resonance, the circuit behaves like a simple resistor, with voltage and current in phase.