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

To solve this problem, we need to understand the concept of modulation index in amplitude modulation (AM). The modulation index (\(m\)) in AM is defined by the formula:

\( m = \frac{A_m}{A_c} \)

where \(A_m\) is the amplitude of the modulating signal, and \(A_c\) is the amplitude of the carrier signal.

1. First Case:

   Here, the modulating signal has an amplitude of \(X \, \text{V}\), and it is superimposed on a carrier signal of amplitude \(Y \, \text{V}\).

   Thus, the modulation index (\(m_1\)) for the first case is:

   \( m_1 = \frac{X}{Y} \)

2. Second Case:

   In this scenario, the same modulating signal with amplitude \(X \, \text{V}\) is superimposed on a different carrier signal of amplitude \(2Y \, \text{V}\).

   The modulation index (\(m_2\)) for the second case is:

   \( m_2 = \frac{X}{2Y} \)

3. Ratio of Modulation Indexes:

   We are asked to find the ratio of the modulation indexes in the two cases, which is \( \frac{m_1}{m_2} \).

   Substituting the values, we get:

   \( \frac{m_1}{m_2} = \frac{\frac{X}{Y}}{\frac{X}{2Y}} = \frac{X}{Y} \times \frac{2Y}{X} = 2 \)

   Thus, the ratio of the modulation index in the two cases is \(2:1\).

Therefore, the correct answer is \(2:1\).