*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, the correct formula is:

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

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

### Explanation of the Correct Answer:
- The Q factor represents the ratio of the reactance to the resistance in a resonant circuit. A higher Q indicates a sharper resonance peak, meaning the circuit is more selective at its resonant frequency.
- In a parallel resonant circuit, the Q is calculated using the resistance divided by the reactance of either the inductor or capacitor, which reflects how effectively the circuit can store energy compared to how much energy is lost.

### Why the Other Choices are Incorrect:
- **Choice A: Reactance of either the inductance or capacitance divided by the resistance**
  - This is incorrect because it reverses the relationship. The Q factor should have resistance in the denominator, not the numerator.

- **Choice B: Reactance of either the inductance or capacitance multiplied by the resistance**
  - This is incorrect as it does not represent the relationship between resistance and reactance in the context of Q. The Q factor is not a product but a ratio.

- **Choice D: Reactance of the inductance multiplied by the reactance of the capacitance**
  - This is incorrect because it does not relate to the Q factor. The Q factor is concerned with resistance and the reactance of either the inductor or capacitor, not their product.

### Useful Formulas and Rules of Thumb:
- For a parallel RLC circuit, the resonant frequency ($f_0$) is given by:

$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

where:
- $L$ = inductance in henries
- $C$ = capacitance in farads

- The Q factor can also be thought of in terms of bandwidth ($BW$) at the resonant frequency:

$$Q = \frac{f_0}{BW}$$

This shows how the Q factor relates to the sharpness of the resonance peak in terms of frequency. 

Understanding these concepts will help you effectively calculate and interpret the Q factor in parallel resonant circuits for your Extra Class exam.