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If a carrier wave $\mathrm{c}(\mathrm{t})=\mathrm{A} \sin \omega_{\mathrm{c}} \mathrm{t}$ is amplitude modulated by a modulator signal $\mathrm{m}(\mathrm{t})=\mathrm{A}$ sin $\omega_{\mathrm{m}} \mathrm{t}$ then the equation of modulated signal $\left[\mathrm{C}_{\mathrm{m}}(\mathrm{t})\right]$ and its modulation index are respectively
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Verified Answer
The correct answer is:
$C_m(t)=A\left(1+\sin \omega_m t\right) \sin \omega_c t$ and 1
$C_m(t)=A\left(1+\sin \omega_m t\right) \sin \omega_c t$ and 1
Modulation index
$$
\mathrm{m}_{\mathrm{a}}=\frac{\mathrm{E}_{\mathrm{m}}}{\mathrm{E}_{\mathrm{c}}}=\frac{\mathrm{A}}{\mathrm{A}}=1
$$
Equation of modulated signal $\left[\mathrm{C}_{\mathrm{m}}(\mathrm{t})\right]$
$$
=\mathrm{E}_{(\mathrm{C})}+\mathrm{m}_{\mathrm{a}} \mathrm{E}_{(\mathrm{C})} \sin \omega_{\mathrm{m}}^{\mathrm{t}}
$$
$=\mathrm{A}\left(1+\sin \mathrm{w}_{\mathrm{C}} \mathrm{t}\right) \sin \omega_{\mathrm{m}} \mathrm{t}$
$\left(\right.$ As $\left.\mathrm{E}_{(\mathrm{C})}=\mathrm{A} \sin \omega_{\mathrm{c}} \mathrm{t}\right)$
$$
\mathrm{m}_{\mathrm{a}}=\frac{\mathrm{E}_{\mathrm{m}}}{\mathrm{E}_{\mathrm{c}}}=\frac{\mathrm{A}}{\mathrm{A}}=1
$$
Equation of modulated signal $\left[\mathrm{C}_{\mathrm{m}}(\mathrm{t})\right]$
$$
=\mathrm{E}_{(\mathrm{C})}+\mathrm{m}_{\mathrm{a}} \mathrm{E}_{(\mathrm{C})} \sin \omega_{\mathrm{m}}^{\mathrm{t}}
$$
$=\mathrm{A}\left(1+\sin \mathrm{w}_{\mathrm{C}} \mathrm{t}\right) \sin \omega_{\mathrm{m}} \mathrm{t}$
$\left(\right.$ As $\left.\mathrm{E}_{(\mathrm{C})}=\mathrm{A} \sin \omega_{\mathrm{c}} \mathrm{t}\right)$
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