An amplitude modulated wave is represented by the expression

Question:

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

 

  1. $5 \mathrm{~V}, 8 \mathrm{~V}$

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

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

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


Correct Option: , 3

Solution:

$\mathrm{V}_{\mathrm{m}}=5(1+0.6 \cos 6280 \mathrm{t}) \sin \left(2 \pi \times 10^{4} \mathrm{t}\right)$

$\mathrm{V}_{\mathrm{m}}=[5+3 \cos 6820 \mathrm{t}] \sin \left(2 \pi \times 10^{4} \mathrm{t}\right)$

$\mathrm{V}_{\text {max. }}=5+3=8$

$\mathrm{~V}_{\text {min. }}=5-3=2$

 

Leave a comment