*Question G5A01:
What happens when inductive and capacitive reactance are equal in a series LC circuit?*  

*Correct Answer is  C: Resonance causes impedance to be very low*  

### AI Response: (may contain errors)  

In a series LC circuit, resonance occurs when the inductive reactance ($X_L$) and capacitive reactance ($X_C$) are equal. At this point, the circuit's impedance is minimized.

1. **Correct Answer: C - Resonance causes impedance to be very low**

   - At resonance, the inductive reactance $X_L = 2\pi f L$ and capacitive reactance $X_C = \frac{1}{2\pi f C}$ cancel each other out because they are equal in magnitude but opposite in phase. This results in the total reactance being zero.
   - The impedance of the circuit is then determined only by the resistance (if any), which is typically very low, making the overall impedance very low.

2. **Why the other choices are incorrect:**

   - **A: Resonance causes impedance to be very high**  
     This is incorrect because, at resonance in a series LC circuit, the impedance is minimized, not maximized.
   
   - **B: Impedance is equal to the geometric mean of the inductance and capacitance**  
     This is incorrect because impedance is not calculated as the geometric mean of inductance and capacitance. Impedance at resonance is determined by resistance, not by inductance or capacitance.
   
   - **D: Impedance is equal to the arithmetic mean of the inductance and capacitance**  
     This is incorrect because impedance is not calculated as the arithmetic mean of inductance and capacitance. At resonance, the impedance is primarily resistive and not related to the mean of inductance and capacitance.

3. **Useful Formulas:**

   - Inductive Reactance: $X_L = 2\pi f L$
   - Capacitive Reactance: $X_C = \frac{1}{2\pi f C}$
   - At resonance: $X_L = X_C \Rightarrow X_L - X_C = 0$

Understanding these concepts will help you recognize that at resonance in a series LC circuit, the impedance is very low due to the cancellation of reactances.