Question:

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

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The modulation index helps in understanding how much the amplitude varies in an amplitude modulated signal relative to its average amplitude.
Updated On: Mar 13, 2025
  • \(0.3\)
  • \(0.25\)
  • \(0.6\)
  • \(0.5\)
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The Correct Option is C

Solution and Explanation

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

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