Question

The maximum amplitude of the modulated wave is 16v and minimum amplitude is 4v. The percentage modulation is
(A) \[25\% \]
(B) \[40\% \]
(C) \[60\% \]
(D) \[75\% \]

Answer 1

Hint: We know that the formula for percentage modulation index is \[{m_a} = \left( {\dfrac{{{E_{\max }} - {E_{\min }}}}{{{E_{\max }} + {E_{\min }}}}} \right) \times 100\]. We will use it to solve this question.

Complete step by step answer:
The formula for percentage modulation is \[{m_a} = \left( {\dfrac{{{E_{\max }} - {E_{\min }}}}{{{E_{\max }} + {E_{\min }}}}} \right) \times 100\]
Now, we will substitute the values of \[{E_{\max }}\] and \[{E_{\min }}\] in the formula.
 \[{m_a} = \left( {\dfrac{{16v - 4v}}{{16v + 4v}}} \right) \times 100\]
 \[ \Rightarrow {m_a} = \left( {\dfrac{{16 - 4}}{{16 + 4}}} \right) \times 100\]
 \[ \Rightarrow {m_a} = \left( {\dfrac{{12}}{{20}}} \right) \times 100\]
 \[ \Rightarrow {m_a} = \left( {\dfrac{{12}}{2}} \right) \times 10\]
 \[ \Rightarrow {m_a} = 6 \times 10\]
 \[ \Rightarrow {m_a} = 60\% \]

So, the percentage modulation is \[60\% \]. Hence, option (c.) is the correct option.

Additional information: The process of changing the amplitude of a carrier wave in accordance with the amplitude of the amplitude of the audio frequency (AF) signal is known as amplitude modulation (AM). The AM frequency of the carrier wave remains unchanged. The amplitude of the modulated wave is varied in accordance with the amplitude of the modulating wave.
The ratio of change of amplitude of the carrier wave to the amplitude of the original carrier wave is called the modulation factor or degree of modulation or modulation index.
Limitations of amplitude modulation:
1. Noisy reception
2. Low efficiency
3. Small operating range
4. Poor audio quality

Note: The formula for percentage frequency modulation is quite similar to percentage amplitude modulation. So, a student might choose the wrong formula, this will result in a wrong answer. Therefore, be careful while writing the formula.