Question

When signal amplitude is equal to the carrier wave amplitude, then the modulation factor is
$\begin{align}
  & A)2 \\
 & B)1 \\
 & C)\dfrac{1}{2} \\
 & D)\dfrac{1}{4} \\
\end{align}$

Answer 1

Hint: We know that modulation factor is nothing but the modulation index, which measures the amount of modulation carried out by the superposition of two signals. Also do we know that modulation index in the case of amplitude modulation relates the amplitudes of both carrier signals as well as the signal itself, which is being modulated. We proceed by considering the similarity in amplitudes of the carrier as well as the signal itself.
Formula used:
$\mu =\dfrac{{{A}_{s}}}{{{A}_{c}}}$

Complete answer:
In amplitude modulation, we know that modulation factor or modulation index is equal to the ratio of amplitudes of the signal itself and the carrier signal. Mathematically, if ${{A}_{s}}$ and ${{A}_{c}}$ represent the amplitudes of the signal which is being modulated and the carrier signal respectively, then, the modulation factor $\mu $ is given by
$\mu =\dfrac{{{A}_{s}}}{{{A}_{c}}}$
Let this be equation 1.
Coming to our question, we are provided that both the signal which is being modulated and the carrier signal have the same amplitudes. Therefore, we can write:
${{A}_{s}}={{A}_{c}}\Rightarrow \dfrac{{{A}_{s}}}{{{A}_{c}}}=1$
Let this be equation 2.
Substituting equation 2 in equation 1, we have
$\mu =\dfrac{{{A}_{s}}}{{{A}_{c}}}=1$
Let this be equation 3.
Clearly, from equation 3, we can conclude that modulation factor/modulation index in the given case is equal to $1$.

Hence, the correct answer is option $B$.

Note:
Amplitude modulation refers to the superposition of two signals with respect to their amplitudes. During amplitude modulation, the amplitude of the message signal is added with the amplitude of the carrier signal to produce an amplitude-modulated signal. Amplitude modulation is usually used to transmit messages with radio carrier signals.