The maximum peak ro peak voltage of an AM wire is `24 mV` and the minimum peak to peak voltage is `8mV`. The modulation factor is

Options

A. `10%`
B. `20%`
C. `25%`
D. `50%`

Explanation

To find the modulation factor for the given AM wave, we will follow these steps:

### Step 1: Identify the maximum and minimum peak-to-peak voltages
- Given:
- Maximum peak-to-peak voltage, \( V_{max} = 24 \, \text{mV} \)
- Minimum peak-to-peak voltage, \( V_{min} = 8 \, \text{mV} \)

### Step 2: Calculate the maximum and minimum voltages
- The maximum voltage \( V_{m} \) is half of the maximum peak-to-peak voltage:
\[ V_{m} = \frac{V_{max}}{2} = \frac{24 \, \text{mV}}{2} = 12 \, \text{mV} \]
- The minimum voltage \( V_{min} \) is half of the minimum peak-to-peak voltage:
\[ V_{min} = \frac{V_{min}}{2} = \frac{8 \, \text{mV}}{2} = 4 \, \text{mV} \]

### Step 3: Calculate the modulation factor
- The modulation factor \( m_a \) is given by the formula:
\[ m_a = \frac{V_{m} - V_{min}}{V_{m} + V_{min}} \]
- Substitute the values:
\[ m_a = \frac{12 \, \text{mV} - 4 \, \text{mV}}{12 \, \text{mV} + 4 \, \text{mV}} = \frac{8 \, \text{mV}}{16 \, \text{mV}} = \frac{1}{2} \]

### Step 4: Convert to percentage
- To express the modulation factor as a percentage:
\[ m_a = 0.5 \text{ or } 50\% \]

### Conclusion
- The modulation factor is \( 0.5 \) or \( 50\% \).

### Final Answer
- The modulation factor is \( 0.5 \) or \( 50\% \).

---