If the maximum amplitude of an amoplitude modulated wave is 25 V and the minimum amplitude is 5V, the modulation index is

Options

A. `1/5`
B. `1/3`
C. `3/2`
D. `2/3`

Explanation

To find the modulation index (μ) of an amplitude modulated 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) = 25 V
- Minimum Amplitude (A_min) = 5 V

2. **Use the Formula for Modulation Index**:
The modulation index (μ) is calculated using the formula:
\[ \mu = \frac{A_{max} - A_{min}}{A_{max} + A_{min}} \]

3. **Substitute the Values into the Formula**:
Substitute the values of A_max and A_min into the formula:
\[ \mu = \frac{25 V - 5 V}{25 V + 5 V} \]

4. **Calculate the Numerator**:
\[ A_{max} - A_{min} = 25 V - 5 V = 20 V \]

5. **Calculate the Denominator**:
\[ A_{max} + A_{min} = 25 V + 5 V = 30 V \]

6. **Calculate the Modulation Index**:
Now substitute the results from the numerator and denominator:
\[ \mu = \frac{20 V}{30 V} = \frac{2}{3} \]

7. **Final Result**:
Therefore, the modulation index (μ) is:
\[ \mu = \frac{2}{3} \approx 0.67 \]