TS EAMCET · Physics · Units and Dimensions

A carrier signal of frequency $v_{1}$ and peak voltage of $V_{1}$ is modulated by a message signal of frequency $v_{2}$ and peak voltage of $V_{2}$ . Let $m$ be the modulation index and $v_{+}, v_{-}$ be side bands produced. The correct statement is

A $m = \frac{V_{1}}{V_{2}}$
B $v_{1} = \frac{v_{+} + v_{-}}{2}$
C $v_{2} = \frac{v_{+} + v_{-}}{2}$
D $m > \frac{V_{2}}{V_{1}}$

Verified Solution

Answer & Solution

Correct Answer

(B) $v_{1} = \frac{v_{+} + v_{-}}{2}$

Step-by-step Solution

Detailed explanation

Given: For carrier signal Frequency v1 and peak voltage V1 For message signal Frequency v2 and peak voltage V2 The modulation index m is defined as the ratio of modulation voltage to the carrier voltage. Thus, m=V2V1. The frequency of the carrier signal is given as, v1=v++v-2

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A carrier signal of frequency v1 and peak voltage of V1 is modulated by a message signal of frequency v2 and peak voltage of V2. Let m be the modulation index and v+,v- be side bands produced. The correct statement is

Step-by-step Solution

A carrier signal of frequency $v_{1}$ and peak voltage of $V_{1}$ is modulated by a message signal of frequency $v_{2}$ and peak voltage of $V_{2}$ . Let $m$ be the modulation index and $v_{+}, v_{-}$ be side bands produced. The correct statement is