Question

For an amplitude modulated wave, the maximum amplitude is found to be $9V$ while the minimum amplitude is found to be $3V$. The modulation index is____________

• A. $100\%$
• B. $75\%$
• C. $50\%$
• D. $25\%$

Answer 1

The correct option is C

$50\%$

Step 1 : Given data

Maximum amplitude $=9V$

Minimum amplitude $=3V$

Step 2 : To find the modulation index

$$\begin{gathered} \mu =\left[\frac{V_{max}-V_{min}}{V_{max}+V_{min}}\right]\times 100 \\ =\left[\frac{9-3}{9+3}\right]\times 100 \\ =6/12\times 100 \\ =50\% \end{gathered}$$

Hence the modulation index $\mu =50\%$

Therefore the correct answer is Option C