For an A.M. wave, the maximum and minimum amplitude is found to be 20V and 4v. Find the modulation index(m).

Options

A. `3//5`
B. `5//3`
C. `2//3`
D. `3//2 `

Explanation

To find the modulation index (m) for an amplitude modulated (AM) wave given the maximum and minimum amplitudes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Maximum amplitude (A_max) = 20 V
- Minimum amplitude (A_min) = 4 V

2. **Use the formula for modulation index (m):**
The modulation index for an AM wave is given by the formula:
\[ m = \frac{A_{max} - A_{min}}{A_{max} + A_{min}} \]

3. **Substitute the values into the formula:**
\[ m = \frac{20 V - 4 V}{20 V + 4 V} \]

4. **Calculate the numerator and denominator:**
- Numerator:
\[ 20 V - 4 V = 16 V \]
- Denominator:
\[ 20 V + 4 V = 24 V \]

5. **Substitute the results back into the formula:**
\[ m = \frac{16 V}{24 V} \]

6. **Simplify the fraction:**
\[ m = \frac{16}{24} = \frac{2}{3} \]

7. **Final result:**
The modulation index (m) is \( \frac{2}{3} \).