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. **Understand the Modulation Index**:
The modulation index (μ) in amplitude modulation is defined as the ratio of the amplitude of the message signal (Am) to the amplitude of the carrier signal (Ac).
\[ \mu = \frac{A_m}{A_c} \]

2. **Identify the Condition for Maximum Modulation Index**:
For amplitude modulation to occur effectively, the amplitude of the carrier signal must be greater than or equal to the amplitude of the message signal. This means:
\[ A_c \geq A_m \]

3. **Determine the Maximum Value**:
The maximum value of the modulation index occurs when the amplitude of the carrier signal is equal to the amplitude of the message signal. Therefore, we can set:
\[ A_c = A_m \]

4. **Substitute into the Modulation Index Formula**:
If \( A_c = A_m \), then substituting this into the modulation index formula gives:
\[ \mu = \frac{A_m}{A_c} = \frac{A_m}{A_m} = 1 \]

5. **Conclusion**:
Thus, the maximum value of the modulation index (μ) in an amplitude modulation system is:
\[ \mu_{\text{max}} = 1 \]

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

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