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If a carrier wave c(t)=A sin $ω_{c} t$ is amplitude modulated by a modulator signal m(t)=A sin $ω_{m} t$ then the equation of modulated signal $[C_{m} (t)]$ and its modulation index are respectively

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$C_{m} (t)$ = $A (1 + \sin ω_{m} t) \sin ω_{c} t$ and 2

$C_{m} (t)$ = $A (1 + \sin ω_{m} t) \sin ω_{m} t$ and 1

$C_{m} (t)$ = $A (1 + \sin ω_{m} t) \sin ω_{c} t$ and 1

$C_{m} (t)$ = $A (1 + \sin ω_{c} t) \sin ω_{m} t$ and 2

answer is C.

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Detailed Solution

Modulation index
$m_{a} = \frac{E_{m}}{E_{c}} = \frac{A}{A} = 1$
Equation of modulated signal $[C_{m} (t)]$
$= E_{(C)} + m_{a} E_{(C)} \sin ω_{m} t$
$= A (1 + \sin ω_{m} t) \sin ω_{c} t$
(As ) $E_{(C)} = A \sin ω_{C} t$

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