If `A_m` and `A_c `are the amplitudes of modulating signal and carrier wave respectively, then modulation index is given by

Options

A. `mu=A_m/A_c`
B. `mu=A_c/A_m`
C. `mu=A_c^2/A_m`
D. `mu=A_m^2/A_c`

Answer

To find the modulation index given the amplitudes of the modulating signal \( A_m \) and the carrier wave \( A_c \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The modulating signal is represented as \( Y_m = A_m \sin(\omega_m t) \), where \( A_m \) is the amplitude of the modulating signal and \( \omega_m \) is its angular frequency.
- The carrier wave is represented as \( Y_c = A_c \sin(\omega_c t) \), where \( A_c \) is the amplitude of the carrier wave and \( \omega_c \) is its angular frequency.

2. **Identify the Formula for Modulation Index**:
- The modulation index (often denoted as \( \mu \)) is defined as the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave.

3. **Write the Formula**:
- Thus, the modulation index is given by:
\[ \mu = \frac{A_m}{A_c} \]

4. **Interpretation**:
- The modulation index is a dimensionless quantity that indicates the extent of modulation. A higher modulation index means a greater degree of modulation.

5. **Percentage Modulation**:
- If needed, the percentage modulation can also be calculated as:
\[ \text{Percentage Modulation} = \left( \frac{A_m}{A_c} \right) \times 100 \]

### Final Answer:
The modulation index \( \mu \) is given by:
\[ \mu = \frac{A_m}{A_c} \]