Question

For an amplitude modulated wave the minimum amplitude is 3V, while the modulation index is 60%. The maximum amplitude of the modulated wave is

• A. 5 V
• B. 10 V
• C. 12 V
• D. 15 V

Answer 1

The Correct Option is C

To solve this problem, we need to understand the concept of amplitude modulation and how modulation affects the amplitude of the wave. The modulation index (m) is defined as the ratio of the maximum amplitude variation to the amplitude of the unmodulated carrier wave. It's given as a percentage but needs to be used as a numerical fraction in calculations.

1. In an amplitude modulated (AM) wave, the modulation index m can be expressed as: m = \frac{A_\text{max} - A_\text{min}}{A_\text{max} + A_\text{min}} where A_\text{max} is the maximum amplitude and A_\text{min} is the minimum amplitude of the modulated wave.
2. We are given:
   • Minimum amplitude, A_\text{min} = 3 \, \text{V}
   • Modulation index, m = 60\% or 0.6 when converted to a decimal.
3. Substitute the known values into the modulation index formula: 0.6 = \frac{A_\text{max} - 3}{A_\text{max} + 3}
4. Cross-multiply to solve for A_\text{max}: 0.6 (A_\text{max} + 3) = A_\text{max} - 3
5. Simplify and solve the equation:
   • Expand: 0.6 A_\text{max} + 1.8 = A_\text{max} - 3
   • Rearrange terms: 1.8 + 3 = A_\text{max} - 0.6 A_\text{max}
   • Simplify further: 4.8 = 0.4 A_\text{max}
   • Divide both sides by 0.4: A_\text{max} = \frac{4.8}{0.4} = 12 \, \text{V}

Thus, the maximum amplitude of the modulated wave is 12 V.

Therefore, the correct answer is: 12 V