Question

If the maximum and minimum amplitudes of a modulated wave are \( 25 \) V and \( 5 \) V respectively, then the modulation index is:

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

Hint:

For amplitude modulation, use: \[ m = \frac{A_{\max} - A_{\min}}{A_{\max} + A_{\min}} \] to compute the modulation index.

Answer 1

The Correct Option is C

Step 1: Modulation Index Formula The modulation index \( m \) for an amplitude-modulated wave is given by: \[ m = \frac{A_{\max} - A_{\min}}{A_{\max} + A_{\min}} \] where: - \( A_{\max} = 25 \) V (maximum amplitude), - \( A_{\min} = 5 \) V (minimum amplitude). Step 2: Calculating \( m \) \[ m = \frac{25 - 5}{25 + 5} \] \[ = \frac{20}{30} \] \[ = \frac{3}{2} \] Conclusion Thus, the correct answer is: \[ \frac{3}{2} \]