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(D) The modulation index $\mu$ is defined as $\mu = \frac{A_m}{A_c}$,where $A_m$ is the peak amplitude of the message signal and $A_c$ is the peak amp

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-$0.2$

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(D) The modulation index $\mu$ is defined as $\mu = \frac{A_m}{A_c}$,where $A_m$ is the peak amplitude of the message signal and $A_c$ is the peak amplitude of the carrier signal.Given that $A_m$ increases by $0.1 \%$ and $A_c$ increases by $0.3 \%$,the new amplitudes are $A_m' = A_m(1 + 0.001) = 1.001 A_m$ and $A_c' = A_c(1 + 0.003) = 1.003 A_c$.The new modulation index $\mu'$ is $\mu' = \frac{1.001 A_m}{1.003 A_c} = \frac{1.001}{1.003} \mu$.The percentage change in the modulation index is given by $\frac{\mu' - \mu}{\mu} 	imes 100$.Substituting the values: $\left( \frac{1.001}{1.003} - 1 ight) 	imes 100 = \left( \frac{1.001 - 1.003}{1.003} ight) 	imes 100 = \frac{-0.002}{1.003} 	imes 100 \approx -0.1994 \% \approx -0.2 \%$.

$A$ message signal is used to modulate a carrier frequency. If the peak voltages of the message signal and carrier signal are increased by $0.1 \%$ and $0.3 \%$ respectively,then the percentage change in the modulation index is

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