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JEE Main 20139 AprilOnline
Exam
JEE Main
Year
2013
Date
9 April
Mode
Online
Subject
Physics
Chapter
Communication System

JEE Main 2013 · 9 April · Online · Physics · Communication System

If a carrier wave c(t)=A ω_ c t is amplitude modulated by a...

If a carrier wave c(t)=Asin⁡ωct\mathrm{c}(\mathrm{t})=\mathrm{A} \sin \omega_{\mathrm{c}} \mathrm{t} is amplitude modulated by a modulator signal m(t)=A\mathrm{m}(\mathrm{t})=\mathrm{A} sin ωmt\omega_{\mathrm{m}} \mathrm{t} then the equation of modulated signal [Cm(t)]\left[\mathrm{C}_{\mathrm{m}}(\mathrm{t})\right] and its modulation index are respectively

Options

  1. ACm(t)=A(1+sin⁡ωmt)sin⁡ωctC_m(t)=A\left(1+\sin \omega_m t\right) \sin \omega_c t and 2
  2. BCm(t)=A(1+sin⁡ωmt)sin⁡ωmtC_m(t)=A\left(1+\sin \omega_m t\right) \sin \omega_m t and 1
  3. CCm(t)=A(1+sin⁡ωmt)sin⁡ωctC_m(t)=A\left(1+\sin \omega_m t\right) \sin \omega_c t and 1
  4. DCm(t)=A(1+sin⁡ωct)sin⁡ωmtC_m(t)=A\left(1+\sin \omega_c t\right) \sin \omega_m t and 2

Correct answer

C. Cm(t)=A(1+sin⁡ωmt)sin⁡ωctC_m(t)=A\left(1+\sin \omega_m t\right) \sin \omega_c t and 1

Step-by-step solution

Modulation index ma=EmEc=AA=\mathrm{m}_{\mathrm{a}}=\frac{\mathrm{E}_{\mathrm{m}}}{\mathrm{E}_{\mathrm{c}}}=\frac{\mathrm{A}}{\mathrm{A}}=1 Equation of modulated signal [Cm(t)]=E(C)+maE(C)sin⁡ωmt=A\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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