Question

If $E_C=20\sin {10}^5\mathrm{\pi t}$ and $E_M=10\sin 400\mathrm{\pi t}$ are carrier and modulating signals respectively, the modulation index is

• A. $56\%$
• B. $30\%$
• C. $50\%$
• D. $48\%$

Answer 1

The correct option is C

$50\%$

Step 1: Given data

Carrier signal, $E_C=20\sin {10}^5\mathrm{\pi t}$

Modulating signal,$E_M=10\sin 400\mathrm{\pi t}$

Step 2: Formula used

Modulation index, $m$ is given by $\frac{amplitudeof{E}_M}{amplitudeof{E}_C}$

Step 3: Substituting the values

$m=\frac{amplitudeof{E}_M}{amplitudeof{E}_C}=\frac{10}{20}\times 100=50\%$

Therefore, the modulation index is $50\%$

Hence, option C is correct