The maximum amplitude for an amplitude modulated wave is found to be 12V while the minimum amplitude is found to be 3V. The modulation index is `0.6x` where x is _____________

Answer

To solve the problem, we need to find the value of \( x \) in the modulation index formula. The modulation index \( \mu \) is given by the formula:

\[ \mu = \frac{V_{\text{max}} - V_{\text{min}}}{V_{\text{max}} + V_{\text{min}}} \]

### Step 1: Identify the maximum and minimum amplitudes
From the problem, we know:
- \( V_{\text{max}} = 12 \, \text{V} \)
- \( V_{\text{min}} = 3 \, \text{V} \)

### Step 2: Substitute the values into the modulation index formula
Substituting the values into the modulation index formula:

\[ \mu = \frac{12 - 3}{12 + 3} \]

### Step 3: Simplify the numerator and denominator
Calculating the numerator and denominator:

\[ \mu = \frac{9}{15} \]

### Step 4: Simplify the fraction
Now, simplify the fraction:

\[ \mu = \frac{3}{5} = 0.6 \]

### Step 5: Relate the modulation index to the given expression
According to the problem, the modulation index is given as \( 0.6x \). Therefore, we can set up the equation:

\[ 0.6x = 0.6 \]

### Step 6: Solve for \( x \)
Dividing both sides by \( 0.6 \):

\[ x = 1 \]

### Final Answer
Thus, the value of \( x \) is \( 1 \).

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