*Question E5A09:
How is the Q of an RLC parallel resonant circuit calculated?*  

*Correct Answer is  C: Resistance divided by the reactance of either the inductance or capacitance*  

### AI Response: (may contain errors)  

To calculate the Q (quality factor) of an RLC parallel resonant circuit, you use the formula:

$$ Q = \frac{R}{X} $$

where:
- $R$ is the resistance in ohms.
- $X$ is the reactance of either the inductance ($X_L$) or the capacitance ($X_C$).

### Explanation:

1. **Correct Answer (C): Resistance divided by the reactance of either the inductance or capacitance**

   - The quality factor $Q$ of a parallel resonant circuit is defined as the ratio of the resistance to the reactance. This is because $Q$ represents how underdamped the circuit is, or how well it can store energy relative to the energy dissipated per cycle. In a parallel circuit, the resistance is in parallel with the reactive components, and the formula reflects this relationship.

2. **Why the Other Choices are Incorrect:**

   - **Choice A: Reactance of either the inductance or capacitance divided by the resistance**
     - This is incorrect because it inverts the relationship. In a parallel circuit, $Q$ is determined by how much resistance is present relative to the reactance, not the other way around.

   - **Choice B: Reactance of either the inductance or capacitance multiplied by the resistance**
     - This is incorrect because multiplying reactance by resistance does not yield a dimensionless quality factor. The units would not cancel out to give a pure number, which is necessary for $Q$.

   - **Choice D: Reactance of the inductance multiplied by the reactance of the capacitance**
     - This is incorrect because multiplying the reactances of the inductance and capacitance does not relate to the quality factor. The $Q$ factor is about the ratio of resistance to reactance, not the product of reactances.

### Useful Formula:

For a parallel resonant circuit, the quality factor $Q$ is given by:

$$ Q = \frac{R}{X_L} = \frac{R}{X_C} $$

where $X_L = 2\pi f L$ and $X_C = \frac{1}{2\pi f C}$, with $f$ being the resonant frequency, $L$ the inductance, and $C$ the capacitance.