JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Semiconductors

A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index?

Answer: (C)

Solution

The envelope of a modulated carrier swings between

A_{m a x} = A_{c} + A_{m}

and

A_{m i n} = A_{c} - A_{m}

. Here the voltage rises to

160 V

and falls to

40 V

, so adding these gives

A_{m a x} + A_{m i n} = 2 A_{c} = 200 V

and subtracting gives

A_{m a x} - A_{m i n} = 2 A_{m} = 120 V

. Thus

A_{c} = 100 V

and

A_{m} = 60 V

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

μ = \frac{A _{m}}{A _{c}} = \frac{60}{100} = 0.6

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Single correct option