An amplitude modulated wave is represented by the expression

Question:

An amplitude modulated wave is represented by the expression $v_{m}=5(1+0.6 \cos 6280 t) \sin \left(211 \times 10^{4} t\right)$ volts The minimum and maximum amplitudes of the amplitude modulated wave are, respectively :

  1. (1) $\frac{3}{2} \mathrm{~V}, 5 \mathrm{~V}$

  2. (2) $\frac{5}{2} \mathrm{~V}, 8 \mathrm{~V}$

  3. (3) $5 \mathrm{~V}, 8 \mathrm{~V}$

  4. (4) $3 \mathrm{~V}, 5 \mathrm{~V}$


Correct Option: , 2

Solution:

(2) From the given expression, $V_{m}=5(1+0.6 \cos 6280 t) \sin \left(211 \times 10^{4} t\right)$

Modulation index, $\mu=0.6$

$\because A_{m}=\mu A_{c}$

$\frac{A_{\max }+A_{\min }}{2}=A_{c}=5$          ...(1)

$\frac{A_{\max }-A_{\min }}{2}=A_{m}=3$         ...(2)

From equation (i) $+$ (ii),

Maximum amplitude, $A_{\max }=8$.

From equation (i) - (ii),

Minimum amplitude $A_{\min }=2$.

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