JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Semiconductors

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In an amplitude modulation, a modulating signal having amplitude of XV is superimposed with a carrier signal of amplitude YV in first case. Then, in second case, the same modulating signal is superimposed with different carrier signal of amplitude 2YV. The ratio of modulation index in the two case respectively will be:

(A) $1 : 2$
(B) $1 : 1$
(C) $2 : 1$ ✓ Correct
(D) $4 : 1$

Answer: (C)

Solution

The modulation index is the ratio of the modulating-signal amplitude to the carrier amplitude,

μ = \frac{A _{m}}{A _{c}}

. With the same modulating amplitude

X

, the first carrier

Y

gives

μ_{1} = \frac{X}{Y}

and the second carrier

2 Y

gives

μ_{2} = \frac{X}{2 Y}

. Their ratio is

\frac{μ _{1}}{μ _{2}} = \frac{X / Y}{X /2 Y} = 2

. The modulation indices in the two cases are in the ratio

2 : 1

JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Single correct option

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JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Semiconductors

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