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## QuestionPhysicsClass 12

For an amplitude modulated wave, the maximum amplitude is found to be $$10V$$ while the minimum amplitude is found to be $$2V$$ . Determine the modulation index, $$\mu$$ .
What would be the value of $$\mu$$  if the minimum amplitude is zero volt?

$$\rightarrow$$ For the first case,
$$A_{\mathit{Max}}=A_M+A_C=10V\quad \dots(i)$$
$$A_{\mathit{Min}}=A_C-A_M=2V\quad \dots(ii)$$
From $$\left(i\right)+\left(\mathit{ii}\right)$$
$$\Rightarrow 2A_C=12$$
$$\Rightarrow A_C=6V$$
From $$\left(i\right)$$
$$\Rightarrow A_M+6=10\Rightarrow A_M=4V$$
Modulation index, $$\mu =\frac{A_M}{A_C}=\frac 4 6=\frac 2 3=0.67$$
$$\rightarrow$$  for the second case we use, $$A_{\mathit{min}}=0$$
$$\Rightarrow A_{\mathit{max}}=A_C+A_M$$
$$\Rightarrow A_C=A_M=5$$
$$\Rightarrow \mu =\frac 5 5=1=100$$