Question

For an amplitude modulated wave, the maximum and minimum amplitudes are found to be \( 10 \) V and \( 2 \) V respectively. Then the modulation index is?

• A. \( \frac{3}{4} \)
• B. \( \frac{1}{5} \)
• C. \( \frac{1}{3} \)
• D. \( \frac{2}{3} \)

Hint:

The modulation index in AM is calculated as \( m = \frac{A_{\max} - A_{\min}}{A_{\max} + A_{\min}} \). A modulation index between 0 and 1 indicates proper amplitude modulation.

Answer 1

The Correct Option is D

Step 1: Understanding the Modulation Index 
The modulation index (\( m \)) in amplitude modulation (AM) is given by: \[ m = \frac{A_{\max} - A_{\min}}{A_{\max} + A_{\min}} \] where: - \( A_{\max} \) is the maximum amplitude, - \( A_{\min} \) is the minimum amplitude. 

Step 2: Substituting Given Values 
Given: \[ A_{\max} = 10 V, \quad A_{\min} = 2 V \] \[ m = \frac{10 - 2}{10 + 2} \] \[ = \frac{8}{12} \] \[ = \frac{2}{3} \] 

Step 3: Verify the Correct Answer 
Thus, the modulation index is \( \frac{2}{3} \), which corresponds to Option (4).