*Question G5A12:
What occurs in an LC circuit at resonance?*  

*Correct Answer is  D: Inductive reactance and capacitive reactance cancel*  

### AI Response: (may contain errors)  

In an LC circuit at resonance, the key characteristic is that the inductive reactance ($X_L$) and capacitive reactance ($X_C$) cancel each other out. This is why the correct answer is:

**D: Inductive reactance and capacitive reactance cancel**

### Explanation:

1. **Why the correct answer is correct:**
   - At resonance, the inductive reactance ($X_L = 2\pi f L$) and capacitive reactance ($X_C = \frac{1}{2\pi f C}$) are equal in magnitude but opposite in phase. This means:
     $$X_L = X_C$$
   - When $X_L$ and $X_C$ cancel each other, the total reactance of the circuit is zero, and the circuit behaves purely resistively.

2. **Why the other choices are incorrect:**
   - **A: Current and voltage are equal**  
     This statement is incorrect because current and voltage are not necessarily equal in magnitude. Instead, at resonance, the impedance is minimized, and the current is maximized for a given voltage.
   
   - **B: Resistance is cancelled**  
     Resistance is not cancelled in an LC circuit at resonance. Only the reactances cancel each other. The resistance remains and determines the circuit's bandwidth and quality factor.
   
   - **C: The circuit radiates all its energy in the form of radio waves**  
     An LC circuit at resonance does not inherently radiate energy as radio waves. It simply oscillates energy between the inductor and capacitor. Radiation would require an antenna or some other radiating structure.

### Useful Formula:

- **Resonant Frequency ($f_0$):**  
  The frequency at which resonance occurs is given by:
  $$f_0 = \frac{1}{2\pi \sqrt{LC}}$$

This formula helps determine the frequency at which the inductive and capacitive reactances cancel each other out.