The maximum value of modulation index in case of amplitude modulation system is

Options

A. 1
B. 0.1
C. 100
D. Infinity

Answer

To find the maximum value of the modulation index in an amplitude modulation (AM) system, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Modulation Index**:
The modulation index (m) in amplitude modulation is defined as the ratio of the amplitude of the message signal (A_m) to the amplitude of the carrier signal (A_c). This can be expressed mathematically as:
\[ m = \frac{A_m}{A_c} \]

2. **Determining Maximum Value**:
The modulation index can take values from 0 to 1. The maximum value occurs when the amplitude of the message signal equals the amplitude of the carrier signal. Therefore, the maximum modulation index can be expressed as:
\[ m_{\text{max}} = \frac{A_m}{A_c} \leq 1 \]

3. **Condition for Maximum Modulation**:
The condition for achieving the maximum modulation index (m = 1) is that the amplitude of the message signal should be equal to the amplitude of the carrier signal. This means that the envelope of the modulated signal will reach its peak value (which is twice the steady state value of the carrier) and will also fall to zero.

4. **Conclusion**:
Therefore, the maximum value of the modulation index in an amplitude modulation system is:
\[ m_{\text{max}} = 1 \]

### Final Answer:
The maximum value of the modulation index in case of an amplitude modulation system is **1**.

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