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. **Understanding Modulation Index**: The modulation index (denoted as \( \mu \) or \( m_a \)) is a measure of the extent of modulation applied to the carrier wave by the modulating signal.

2. **Defining the Amplitudes**:
- Let \( A_m \) be the amplitude of the modulating signal.
- Let \( A_c \) be the amplitude of the carrier wave.

3. **Formula for Modulation Index**: The modulation index is defined as the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave. This can be mathematically expressed as:
\[ \mu = \frac{A_m}{A_c} \]

4. **Interpreting the Result**:
- If \( \mu > 1 \), it indicates over modulation.
- If \( \mu = 1 \), it indicates critical modulation.
- If \( \mu < 1 \), it indicates under modulation.

5. **Conclusion**: Therefore, the modulation index is given by the formula:
\[ \mu = \frac{A_m}{A_c} \]