A carrier wave of amplitude A is used to modulate (amplitude) the signal.Modulated signal amplitude swings from 0.1 A to 1.9A,calculate modulation index.`

Answer

To calculate the modulation index for the given modulated signal, we will follow these steps:

### Step 1: Understand the Modulation Index Formula
The modulation index (μ) is defined as the ratio of the amplitude of the modulating signal (A_m) to the amplitude of the carrier signal (A_c).
\[ \mu = \frac{A_m}{A_c} \]

### Step 2: Identify the Given Information
From the problem, we know:
- The modulated signal amplitude swings from 0.1A to 1.9A.
- This means:
- The maximum amplitude (A_max) = 1.9A
- The minimum amplitude (A_min) = 0.1A

### Step 3: Calculate the Amplitude of the Modulating Signal (A_m)
The amplitude of the modulating signal (A_m) can be calculated using the formula:
\[ A_m = \frac{A_{max} - A_{min}}{2} \]
Substituting the values:
\[ A_m = \frac{1.9A - 0.1A}{2} = \frac{1.8A}{2} = 0.9A \]

### Step 4: Calculate the Amplitude of the Carrier Signal (A_c)
The amplitude of the carrier signal (A_c) can be calculated using the formula:
\[ A_c = \frac{A_{max} + A_{min}}{2} \]
Substituting the values:
\[ A_c = \frac{1.9A + 0.1A}{2} = \frac{2.0A}{2} = 1.0A \]

### Step 5: Calculate the Modulation Index (μ)
Now that we have both A_m and A_c, we can calculate the modulation index:
\[ \mu = \frac{A_m}{A_c} = \frac{0.9A}{1.0A} = 0.9 \]

### Final Answer
The modulation index (μ) is 0.9.

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