*Question E5A02:
What is the resonant frequency of an RLC circuit if R is 22 ohms, L is 50 microhenries, and C is 40 picofarads?*  

*Correct Answer is  C: 3.56 MHz*  

### AI Response: (may contain errors)  

To find the resonant frequency of an RLC circuit, we use the formula for the resonant frequency of a series or parallel RLC circuit:

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

where:
- $f_0$ is the resonant frequency in hertz (Hz),
- $L$ is the inductance in henries (H),
- $C$ is the capacitance in farads (F).

Given:
- $L = 50$ microhenries = $50 \times 10^{-6}$ H,
- $C = 40$ picofarads = $40 \times 10^{-12}$ F.

Substitute these values into the formula:

$$
f_0 = \frac{1}{2\pi\sqrt{(50 \times 10^{-6})(40 \times 10^{-12})}}
$$

Calculate the product of $L$ and $C$:

$$
LC = (50 \times 10^{-6}) \times (40 \times 10^{-12}) = 2 \times 10^{-15}
$$

Now, calculate the square root:

$$
\sqrt{LC} = \sqrt{2 \times 10^{-15}} = 1.414 \times 10^{-7.5}
$$

Finally, calculate the resonant frequency:

$$
f_0 = \frac{1}{2\pi \times 1.414 \times 10^{-7.5}} \approx 3.56 \times 10^6 \text{ Hz} = 3.56 \text{ MHz}
$$

### Explanation of Choices:
- **A: 44.72 MHz**  
  This choice is incorrect because it results from a miscalculation, possibly due to incorrect handling of the units or the square root.

- **B: 22.36 MHz**  
  This choice is incorrect for similar reasons as choice A. It does not match the correct calculation of the resonant frequency.

- **C: 3.56 MHz**  
  This is the correct answer, as shown by the calculation above.

- **D: 1.78 MHz**  
  This choice is incorrect and could result from a calculation error, such as dividing by $2\pi$ incorrectly or miscalculating the square root.

### Key Points:
- The resonant frequency is determined by the values of inductance and capacitance, not resistance.
- Ensure units are correctly converted to henries and farads before calculation.
- Use the formula $f_0 = \frac{1}{2\pi\sqrt{LC}}$ to find the resonant frequency.