An `L-C-R` series circuit has a maximum current of `5A`. If `L=0.5H` and `C=8muF`, then the angular frequency of `AC` voltage is

Options

A. `500 rad//s`
B. `5000rad//s`
C. `400 rad//s`
D. `250 rad//s`

Explanation

To find the angular frequency of the AC voltage in an L-C-R series circuit, we can use the formula:

\[ \omega = \frac{1}{\sqrt{L \cdot C}} \]

where:
- \(\omega\) is the angular frequency in radians per second,
- \(L\) is the inductance in henries (H),
- \(C\) is the capacitance in farads (F).

### Step-by-Step Solution:

1. **Identify the given values**:
- Inductance, \(L = 0.5 \, \text{H}\)
- Capacitance, \(C = 8 \, \mu\text{F} = 8 \times 10^{-6} \, \text{F}\)

2. **Substitute the values into the formula**:
\[ \omega = \frac{1}{\sqrt{L \cdot C}} = \frac{1}{\sqrt{0.5 \cdot 8 \times 10^{-6}}} \]

3. **Calculate \(L \cdot C\)**:
\[ L \cdot C = 0.5 \cdot 8 \times 10^{-6} = 4 \times 10^{-6} \, \text{H}\cdot\text{F} \]

4. **Take the square root**:
\[ \sqrt{L \cdot C} = \sqrt{4 \times 10^{-6}} = 2 \times 10^{-3} \, \text{s} \]

5. **Calculate \(\omega\)**:
\[ \omega = \frac{1}{2 \times 10^{-3}} = 500 \, \text{rad/s} \]

6. **Final answer**:
The angular frequency of the AC voltage is \(500 \, \text{rad/s}\).

### Conclusion:
The correct option is \(500 \, \text{rad/s}\).