JEE Main & Advanced Sample Paper JEE Main Sample Paper-4

  • question_answer
    The antenna current of an AM transmitter is 8A when only the carrier is sent, but it increases to 8 -93A when the carries is modulated by single sine wave. Find the modulation index.

    A)  0.601                   

    B)  0.701   

    C)  0.801                   

    D)  0.501

    Correct Answer: B

    Solution :

    Let \[{{E}_{C}}\And m{{E}_{C}}\] are amplitude volt of carrier wave & modulated wave respectively, than \[{{P}_{C}}=\frac{E_{C}^{2}}{2R}\]Power of transmitted wave, \[{{P}_{T}}={{P}_{C}}+{{P}_{S}}=\frac{E_{C}^{2}}{2R}+\frac{{{m}^{2}}E_{C}^{2}}{4R}\]where \[{{P}_{S}}\] is the power of side bands. \[\frac{{{P}_{T}}}{{{P}_{C}}}=1+\frac{{{m}^{2}}}{2}\] \[\Rightarrow \]\[{{\left( \frac{{{I}_{T}}}{{{I}_{C}}} \right)}^{2}}=1+\frac{{{m}^{2}}}{2}\]\[\Rightarrow \]\[{{\left( \frac{8.93}{8} \right)}^{2}}=1+\frac{{{m}^{2}}}{2}\] \[\Rightarrow \]\[m=0.701\]

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