Question

Question #83928

Answer 1

`9V" peak"`

Explanation:

From the text of the question it is clear that this pertains to Amplitude Modulation.

Modulation index `m` is a dimensionless quantity and is defined as the ratio of amplitudes of the modulating signal and of carrier. mathematically it can be stated as

`m=E_m/E_C`

modulation index `m` takes values between `0 and 1` and no distortion is introduced in the AM wave when
`E_m <= E_C`.

However, for `E_m > E_C`, `m` becomes greater than `1`.
This will distort the the AM signal and is called over modulation.

Sometimes, this modulation index is expressed as a percentage and called as percentage modulation.

`"Percent modulation"=E_m/E_Cxx100`

As shown in the figure, inserting given values we get
`75=E_m/12 xx100`
`=>E_m=75/100 xx12`
`=>E_m=9V" peak"`

-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-

Sometimes we express `Em and Ec` in terms of `E_max and E_min` as seen on a screen of a CRO.

As shown in the figure
`E_m=(E_max-E_min)/2`
and `E_C=E_max-E_m`
Using expression for `E_m` we get
`E_C=(E_max+E_min)/2`

these give
`m=(E_max-E_min)/(E_max+E_min)`