Question

An amplitude modulated wave is represented by the equation $V_m=5(1+0.6\cos 6280t)\sin (211\times {10}^{4}t)\text{V}$. The minimum and maximum amplitudes of the amplitude modulated wave are, respectively :

• A. $\frac{3}{2}\text{V},5\text{V}$
• B. $2\text{V},8\text{V}$
• C. $5\text{V},8\text{V}$
• D. $3\text{V},5\text{V}$

Answer 1

The correct option is B $2\text{V},8\text{V}$

The general expression of an amplitude modulated wave is given by,

$V_m=A_c(1+\mu \cos {\omega }_{m}t)\sin {\omega }_{c}t$

The maximum amplitude is given by,

$A_{max}=A_c(1+\mu )$

The minimum amplitude is given by,

$A_{min}=A_c(1-\mu )$

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

$\text{Modulation index,}\mu =0.6$

$A_c=5\text{V}$

$\Rightarrow A_{max}=5(1+0.6)=8\text{V}$

$\Rightarrow A_{min}=5(1-0.6)=2\text{V}$

Hence, option $\left(B\right)$ is correct.