The maximum amplitude of an AM wave is found to be 15 V while its minimum amplitude is found to be 3 V.What is the modulation index?

Options

A. `(3)/(2)`
B. `(2)/(3)`
C. `(1)/(2)`
D. `(1)/(3)`

Explanation

To find the modulation index of an Amplitude Modulated (AM) wave, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Maximum and Minimum Amplitudes:**
- Given:
- Maximum amplitude (A_max) = 15 V
- Minimum amplitude (A_min) = 3 V

2. **Calculate the Modulation Index (μ):**
- The formula for the modulation index (μ) in AM is given by:
\[ \mu = \frac{A_{max} - A_{min}}{A_{max} + A_{min}} \]
- Substitute the values into the formula:
\[ \mu = \frac{15 V - 3 V}{15 V + 3 V} \]

3. **Perform the Calculations:**
- Calculate the numerator:
\[ 15 V - 3 V = 12 V \]
- Calculate the denominator:
\[ 15 V + 3 V = 18 V \]
- Now substitute these results back into the modulation index formula:
\[ \mu = \frac{12 V}{18 V} \]

4. **Simplify the Fraction:**
- Simplify \(\frac{12}{18}\):
\[ \mu = \frac{2}{3} \]

5. **Conclusion:**
- The modulation index (μ) is \(\frac{2}{3}\).

### Final Answer:
The modulation index is \(\frac{2}{3}\).