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A 1000 W carrier is amplitude-modulated and has a side-band power of 300 W. The depth of modulation is:
1. 0.255
2. 0.545
3. 0.775
4. 0.95

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Correct Answer - Option 3 : 0.775

Concept: 

The total transmitted power for an AM system is given by:

\({P_t} = {P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)\)

Pc = Carrier Power

μ = Modulation Index

Power in side band is given by

\({P_{SB}} = {P_c}\left( {\frac{{{\mu ^2}}}{2}} \right)\)

Calculation:

Side-band power (PSB) = 300 W

Carrier power (PC) = 1000 W

\(\frac{{{P_{SB}}}}{{{P_c}}} = \left( {\frac{{{\mu ^2}}}{2}} \right)\)

\(⇒\frac{{300}}{{1000}} = \left( {\frac{{{\mu ^2}}}{2}} \right)\)

⇒ μ = 0.775

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