If a message signal of frequency $10 \mathrm{kHz}$ and peak voltage $12 \mathrm{~V}$ is used to modulate a…

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
  1. decreased by $25 \%$
  2. increased by $25 \%$
  3. decreased by $20 \%$
  4. increased by $20 \%$

Solution

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
$\Delta V=20-16=4 \mathrm{~V}$
$\% \text { change }=\frac{4}{20} \times 100 \%=20 \%(\text { decrement })$

Asked in: AP EAMCET 2018 (22 Apr Shift 1)

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