The inductor in a `L-C` oscillation has a maximum potential difference of `16V` and maximum energy of `640 mu J`. Find the value of capacitor in `muF` in `L-C` circuit.

Explanation

To find the value of the capacitor in an L-C circuit given the maximum potential difference and maximum energy, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Maximum potential difference (V) = 16 V
- Maximum energy (U) = 640 µJ = 640 × 10^(-6) J

2. **Use the Formula for Energy in a Capacitor**:
The energy stored in a capacitor is given by the formula:
\[ U = \frac{1}{2} C V^2 \]
where \( C \) is the capacitance in farads and \( V \) is the potential difference.

3. **Rearrange the Formula to Solve for Capacitance (C)**:
Rearranging the formula gives:
\[ C = \frac{2U}{V^2} \]

4. **Substitute the Known Values**:
Substitute \( U = 640 × 10^{-6} \) J and \( V = 16 \) V into the equation:
\[ C = \frac{2 \times 640 \times 10^{-6}}{16^2} \]

5. **Calculate the Denominator**:
Calculate \( 16^2 \):
\[ 16^2 = 256 \]

6. **Calculate the Capacitance**:
Now substitute back into the equation:
\[ C = \frac{1280 \times 10^{-6}}{256} \]
\[ C = 5 \times 10^{-6} \text{ F} \]

7. **Convert to Microfarads**:
Since \( 1 \text{ F} = 10^6 \text{ µF} \):
\[ C = 5 \text{ µF} \]

### Final Answer:
The value of the capacitor in the L-C circuit is **5 µF**.