Question

Assertion:The modulation index (or modulation depth) of a modulation scheme describes how much the modulated variable of the carrier signal varies around its normal modulated level.
Reason:In plate modulation, the plate voltage of the RF amplifier is modulated with the audio signal. The audio power requirement is$50$ percent of the RF-carrier power.
(A) Both Assertion and Reason are correct and reason is the correct explanation for Assertion
(B) Both Assertion and Reason are correct but reason is not the correct explanation for Assertion
(C) Assertion is correct, but Reason is incorrect
(D) Both Assertion and Reason are incorrect

Answer 1

Hint:
Focus on the definition of the modulation index. Then try to find out if it has any relation with the Plate modulation.
Formula used:
$\Rightarrow m = \dfrac{{{A_m}}}{{{A_c}}}$, where $m$is the modulation index, ${A_m} = $Amplitude of the message signal, and ${A_c} = $Amplitude of the carrier signal

Complete step by step answer:
The equation of the career signal, in the amplitude modulation is given by
$\Rightarrow c(t) = {A_c}\left( {1 + \dfrac{{{A_m}}}{{{A_c}}}\sin {\omega _m}t} \right)\sin {\omega _c}t$, where${A_m} = $Amplitude of the modulated signal, ${A_c} = $Amplitude of the carrier signal, and ${\omega _c}$is the frequency of the carrier signal.
As we know, the modulation index (or modulation depth) is given by
$\Rightarrow m = \dfrac{{{A_m}}}{{{A_c}}}$
The modulation index describes the extent to which the modulation is performed on the message signal.
As it is the ratio of the Amplitude of the message signal to the Amplitude of the carrier signal, it indicates the amount by which the modulated variable of the carrier signal varies around its normal modulated level.
$\therefore $ The Assertion is correct.
Also, we know that in plate modulation, the plate voltage of the RF amplifier is modulated with the audio signal. The audio power requirement is$50$ percent of the RF-career power.
$\therefore $ The Reason is also correct.
But the assertion is an implication of the basic definition of the modulation index. The plate modulation has nothing to do with the definition of the modulation of the modulation index.
Hence, the correct answer is option (B), Both Assertion and Reason are correct but reason is not the correct explanation for Assertion.

Note:
We are not required to have the in-depth knowledge of each and every modulation scheme. Only the basic concept of modulation index should be clear. It may be defined differently in each modulation scheme, but its basic concept is common.