For an amplitude modulated wave, the minimum amplitude is 3 V, while the modulation index is 60. The maximum amplitude of the modulated wave is:

Given: modulation index m = 0.6 and minimum amplitude A = 3 V. Find: maximum amplitude A of the amplitude modulated wave. For an amplitude modulated wave, A = Ac(1+m), A = Ac(1-m) Using the given minimum amplitude, 3 = Ac(1-0.6) = 0.4Ac So, Ac = 30.4 = 7.5 V Now, A = 7.5(1+0.6) = 7.5 1.6 = 12 V Therefore, the maximum amplitude of the modulated wave is 12 V. The correct option is B.

For an amplitude modulated wave, the minimum amplitude is 3 V, wh… — Solution | JEE Physics

MCQEasyJEE 2023Electromagnetic Spectrum & Applications

For an amplitude modulated wave, the minimum amplitude is $3 \, \text{V}$ , while the modulation index is $60\%$ . The maximum amplitude of the modulated wave is:

A
$10 \, \text{V}$
B
$12 \, \text{V}$
C
$15 \, \text{V}$
D
$5 \, \text{V}$

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: modulation index $m = 0.6$ and minimum amplitude $A_{\min} = 3 \, \text{V}$ .

Find: maximum amplitude $A_{\max}$ of the amplitude modulated wave.

For an amplitude modulated wave,

A_{\max} = A_c(1+m), \qquad A_{\min} = A_c(1-m)

Using the given minimum amplitude,

3 = A_c(1-0.6) = 0.4A_c

So,

A_c = \frac{3}{0.4} = 7.5 \, \text{V}

Now,

A_{\max} = 7.5(1+0.6) = 7.5 \times 1.6 = 12 \, \text{V}

Therefore, the maximum amplitude of the modulated wave is $12 \, \text{V}$ . The correct option is B.

Common mistakes

Using $A_{\min} = A_c$ is incorrect because the minimum envelope amplitude in amplitude modulation is $A_c(1-m)$ . Always include the modulation index while relating minimum or maximum amplitude to the carrier amplitude.
Taking $60\%$ as $60$ instead of $0.6$ gives a completely wrong result. Convert percentage modulation index to decimal before substitution.
Matching the final value with the marked answer without checking the calculation is incorrect. The solution contains inconsistent intermediate steps, so the amplitude-modulation relations must be applied carefully to verify the correct option.

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Answer

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