Question

If in an amplitude modulated wave, the maximum amplitude is 14 V and the modulation index is 0.4, then the amplitude of the carrier wave is

• A. 4 V
• B. 8 V
• C. 12 V
• D. 10 V

Hint:

For amplitude modulated waves, use the formula: \( A_c = \frac{A_{max}}}{1 + m} \) where \( m \) is the modulation index.

Answer 1

The Correct Option is D

Step 1: Use the relation between modulation index and amplitudes.
The modulation index \( m \) is given by: \[ m = \frac{A_m}{A_c} \] Where: \[ A_m = \text{Amplitude of modulating signal}, \quad A_c = \text{Amplitude of carrier wave} \] The maximum amplitude of the AM wave is: \[ A_{\text{max}} = A_c + A_m \Rightarrow A_m = A_{\text{max}} - A_c \] Substitute into modulation index formula: \[ m = \frac{A_{\text{max}} - A_c}{A_c} \Rightarrow mA_c = A_{\text{max}} - A_c \Rightarrow A_c (1 + m) = A_{\text{max}} \] Step 2: Insert values.
\[ A_{\text{max}} = 14\, \text{V}, \quad m = 0.4 \Rightarrow A_c = \frac{14}{1 + 0.4} = \frac{14}{1.4} = 10\, \text{V} \] Step 3: Select the correct option.
The amplitude of the carrier wave is 10 V, which matches option (4).