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If a message signal of frequency $10 \mathrm{kHz}$ and peak voltage $12 \mathrm{~V}$ is used to modulate a carrier wave of frequency $1 \mathrm{MHz}$, the modulation index is 0.6 . To make the modulation index 0.75 , the carrier peak voltage should be
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decreased by $20 \%$
Modulation index, $M=\frac{V_{\text {peak, signal }}}{V_{\text {peak, carrier }}}$
Let's write $V_{\text {peak, carrier }}=V$
In first case, $0.6=\frac{12}{V}$
$\Rightarrow \quad V=20 \mathrm{~V}$
In second case, $0.75=\frac{12}{V^{\prime}}$
$\Rightarrow \quad V^{\prime}=\frac{12}{0.75}=16 \mathrm{~V}$
Change in peak voltage of carrier wave
$\Delta V=20-16=4 \mathrm{~V}$
$\% \text { change }=\frac{4}{20} \times 100 \%=20 \%(\text { decrement })$
Let's write $V_{\text {peak, carrier }}=V$
In first case, $0.6=\frac{12}{V}$
$\Rightarrow \quad V=20 \mathrm{~V}$
In second case, $0.75=\frac{12}{V^{\prime}}$
$\Rightarrow \quad V^{\prime}=\frac{12}{0.75}=16 \mathrm{~V}$
Change in peak voltage of carrier wave
$\Delta V=20-16=4 \mathrm{~V}$
$\% \text { change }=\frac{4}{20} \times 100 \%=20 \%(\text { decrement })$
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