A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index?

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JEE Mains Previous Paper 1 (Held On: 12 Jan 2019 Shift 1)
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  1. 0.4
  2. 0.5
  3. 0.6
  4. 0.3

Answer (Detailed Solution Below)

Option 3 : 0.6
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JEE Main 04 April 2024 Shift 1
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90 Questions 300 Marks 180 Mins

Detailed Solution

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Concept:

Modulation index is given as:

\(\Rightarrow {\rm{\mu }} = \frac{{{{\rm{A}}_{{\rm{max}}}} - {{\rm{A}}_{{\rm{min}}}}}}{{{{\rm{A}}_{{\rm{max}}}} + {{\rm{A}}_{{\rm{min}}}}}} = \frac{{{{\rm{V}}_{{\rm{max}}}} - {{\rm{V}}_{{\rm{min}}}}}}{{{{\rm{V}}_{{\rm{max}}}} + {{\rm{V}}_{{\rm{min}}}}}}\)

where Vmax is the maximum voltage and

and Vmin is the minimum voltages.

Calculation:

\(\Rightarrow {\rm{\mu }} = \frac{{160 - 40}}{{160 + 40}} = \frac{{120}}{{200}}\)

∴ μ = 0.6
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