Which one of the following best describes the above signal?
[JEE Main Online Paper (Held on 11-jan-2019 Evening)]
A) \[(9+\sin (2\pi \times {{10}^{4}}t))\sin (2.5\pi \times {{10}^{5}}t)V\]
B) \[(9+\sin (2.5\pi \times {{10}^{5}}t))\sin (2\pi \times {{10}^{4}}t)V\]
C) \[(9+\sin (4\pi \times {{10}^{4}}t))\sin (5\pi \times {{10}^{5}}t)V\]
D) \[(1+9\sin (2\pi \times {{10}^{4}}t))\sin (2.5\pi \times {{10}^{5}}t)V\]
Correct Answer: A
Solution :
Amplitude of AM wave varies as 8 V to 10 V or \[(9\pm 1V)\] Time period of modulating signal,\[{{T}_{m}}\] \[=100\mu s={{10}^{-4}}s\] Time period of carrier signal,\[{{T}_{c}}=8\mu s\] \[=8\times {{10}^{-6}}s\] Hence the signal can be represented as \[C=\left( A+a\sin \frac{2\pi }{{{T}_{m}}}t \right)\sin \frac{2\pi }{{{T}_{C}}}t\] \[=[9+1sin(2\pi \times {{10}^{4}}t)]sin(2.5\pi \times {{10}^{5}}t)V\]
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