Question

For an amplitude modulated wave, the maximum and minimum amplitudes are respectively 16 V and 4 V. The modulation index is:

• A. \(0.3\)
• B. \(0.25\)
• C. \(0.6\)
• D. \(0.5\)

Hint:

The modulation index helps in understanding how much the amplitude varies in an amplitude modulated signal relative to its average amplitude.

Answer 1

The Correct Option is C

In amplitude modulation (AM), the modulation index (\(\mu\)) describes the extent of amplitude variation relative to the unmodulated carrier.
It is defined in terms of the maximum amplitude (\(A_{max}\)) and minimum amplitude (\(A_{min}\)) of the modulated wave as follows: \[ \mu = \frac{A_{max} - A_{min}}{A_{max} + A_{min}} \] Given values from the problem statement are: 
- Maximum amplitude, \(A_{max} = 16 \, V\) 
- Minimum amplitude, \(A_{min} = 4 \, V\) 
Substituting these values into the modulation index formula: \[ \mu = \frac{16 \, V - 4 \, V}{16 \, V + 4 \, V} = \frac{12 \, V}{20 \, V} = \frac{12}{20} = \frac{3}{5} = 0.6 \] The modulation index is 0.6. Comparing this with the given options, option (3) matches our calculated value. 
Correct Answer: (3) 0.6