Question

100% modulation in FM means
\[{\mathbf{A}}.\;\;\;\;{\mathbf{Actual}}{\text{ }}{\mathbf{frequency}}{\text{ }}{\mathbf{deviation}}{\text{ }} > {\text{ }}{\mathbf{maximum}}{\text{ }}{\mathbf{allowed}}{\text{ }}{\mathbf{frequency}}{\text{ }}{\mathbf{deviation}}\]
\[{\mathbf{B}}.\;\;\;\;{\mathbf{Actual}}{\text{ }}{\mathbf{frequency}}{\text{ }}{\mathbf{deviation}}{\text{ }} = {\text{ }}{\mathbf{maximum}}{\text{ }}{\mathbf{allowed}}{\text{ }}{\mathbf{frequency}}{\text{ }}{\mathbf{deviation}}\]
\[{\mathbf{C}}.\;\;\;\;{\mathbf{Actual}}{\text{ }}{\mathbf{frequency}}{\text{ }}{\mathbf{deviation}}{\text{ }} \geqslant {\text{ }}{\mathbf{maximum}}{\text{ }}{\mathbf{allowed}}{\text{ }}{\mathbf{frequency}}{\text{ }}{\mathbf{deviation}}\]
\[{\mathbf{D}}.\;\;\;\;{\mathbf{Actual}}{\text{ }}{\mathbf{frequency}}{\text{ }}{\mathbf{deviation}}{\text{ }} \leqslant {\text{ }}{\mathbf{maximum}}{\text{ }}{\mathbf{allowed}}{\text{ }}{\mathbf{frequency}}{\text{ }}{\mathbf{deviation}}\]

Answer 1

Hint:
Carrier wave is a continuous electromagnetic wave having a constant amplitude and frequency. It does not carry any information itself. Signal wave is a wave that carries information by either varying frequency or varying amplitude. Modulation is defined as the process of varying one or multiple properties of a carrier wave by superimposing it with a signal wave.
When the signal wave has constant amplitude but varying frequency, the signal wave is said to be Frequency Modulated. Similarly, When the signal wave has constant frequency but varying amplitude, the signal wave is said to be Amplitude Modulated.
FM stands for Frequency Modulation. So, Frequency Modulation is aptly defined as changing the frequency of the carrier wave by superimposing the signal wave on top of it.

$m = \dfrac{{Actual{\text{ }}frequency{\text{ }}deviation}}{{Maximum{\text{ }}allowed{\text{ }}frequency{\text{ }}deviation}} \times 100\% $
where m is the modulation percentage.
The above formula can also be used for amplitude modulation. In that case, we replace frequency with amplitude.

Complete step by step solution:
Now, we know the formula of modulation percentage as
$m = \dfrac{{Actual{\text{ }}frequency{\text{ }}deviation}}{{Maximum{\text{ }}allowed{\text{ }}frequency{\text{ }}deviation}} \times 100\% $
Given in question that modulation percentage is \[100\% \]
Inserting the value of modulation percentage in the above equation,
We get,
$100\% = \dfrac{{Actual{\text{ }}frequency{\text{ }}deviation}}{{Maximum{\text{ }}allowed{\text{ }}frequency{\text{ }}deviation}} \times 100\% $
Now cancelling \[100\% \]from Left-Hand Side and Right-Hand Side,
We get,
$1 = \dfrac{{Actual{\text{ }}frequency{\text{ }}deviation}}{{Maximum{\text{ }}allowed{\text{ }}frequency{\text{ }}deviation}}$
Bringing Maximum allowed frequency deviation from Right-Hand Side to Left-Hand Side,
\[Maximum{\text{ }}allowed{\text{ }}frequency{\text{ }}deviation = Actual{\text{ }}frequency{\text{ }}deviation\]

Hence, Option (B) is correct.


Note:
After the second step, where we cancel out \[100\% \] from Left-Hand Side to Right-Hand Side, care must be taken to write 1 in the Left-Hand Side and not 0. Many students perform this silly mistake in a hurry.