When m=1 ,power carried by side bands is:

Options

A. 11.1% of the total power of AM wave
B. 22.2% of the total power of AM wave
C. 33.3% of the total power of AM wave
D. 44.4% of the total power of AM wave

Answer

To solve the problem of finding the power carried by the sidebands when \( m = 1 \), we can follow these steps:

### Step 1: Understand the formula for power in AM wave
The power carried by the sidebands in an Amplitude Modulated (AM) wave is given by the formula:

\[ \frac{P_{sidebands}}{P_{AM}} = \frac{m^2}{m^2 + 2} \]

where:
- \( P_{sidebands} \) is the power in the sidebands,
- \( P_{AM} \) is the total power of the AM wave,
- \( m \) is the modulation index.

### Step 2: Substitute the value of \( m \)
Given that \( m = 1 \), we substitute this value into the formula:

\[ \frac{P_{sidebands}}{P_{AM}} = \frac{1^2}{1^2 + 2} = \frac{1}{1 + 2} = \frac{1}{3} \]

### Step 3: Convert to percentage
To find the percentage of the power carried by the sidebands, we multiply the result by 100:

\[ \text{Percentage of power in sidebands} = \left(\frac{1}{3}\right) \times 100 = \frac{100}{3} \approx 33.33\% \]

### Step 4: Conclusion
Thus, the power carried by the sidebands when \( m = 1 \) is approximately \( 33.33\% \).

### Final Answer
The power carried by the sidebands is \( 33.33\% \).

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