Question

In an amplitude modulation, a modulating signal having amplitude of \(X V\) is superimposed with a carrier signal of amplitude \(Y V\) in first case. Then, in second case, the same modulating signal is superimposed with different carrier signal of amplitude \(2 YV\). The ratio of modulation index in the two cases respectively will be :

• A. $2: 1$
• B. $1: 2$
• C. $1: 1$
• D. $4: 1$

Hint:

 Remember the formula for the modulation index. It is a crucial parameter in amplitude modulation.

Answer 1

The Correct Option is A

Step 1: Recall the Formula for Modulation Index

The modulation index (\( \mu \)) is defined as the ratio of the amplitude of the modulating signal (\( A_m \)) to the amplitude of the carrier signal (\( A_c \)):

\[ \mu = \frac{A_m}{A_c} \]

Step 2: Calculate the Modulation Index for the First Case

In the first case, \( A_m = X \) and \( A_c = Y \). So, the modulation index is:

\[ \mu_1 = \frac{X}{Y} \]

Step 3: Calculate the Modulation Index for the Second Case

In the second case, \( A_m = X \) and \( A_c = 2Y \). So, the modulation index is:

\[ \mu_2 = \frac{X}{2Y} \]

Step 4: Find the Ratio of the Modulation Indices

The ratio of the modulation indices is:

\[ \frac{\mu_1}{\mu_2} = \frac{\frac{X}{Y}}{\frac{X}{2Y}} = \frac{X}{Y} \times \frac{2Y}{X} = 2:1 \]

Conclusion: The ratio of the modulation index in the two cases is \( 2 : 1 \) (Option 1).