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A message of frequency 5 kHz and peak voltage of 2 V is used to modulate a carrier wave of frequency 2 MHz and a peak voltage of 10 V. The modulation index is​
  • a)
    0.01
  • b)
    0.2
  • c)
    0.1
  • d)
    1
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A message of frequency 5 kHz and peak voltage of 2 V is used to modula...
It's very simple.

Use formula, Em/ Ec.

where,
(Em-peak voltage of message signal.
Ec - Peak voltage of carrier wave.)

Am = 2/10
= 0.2
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Community Answer
A message of frequency 5 kHz and peak voltage of 2 V is used to modula...
To find the modulation index, we need to understand the concept of modulation and how it affects the carrier wave. Modulation is the process of modifying a high-frequency carrier wave with a lower-frequency message signal to transmit information. In this case, the message signal has a frequency of 5 kHz and a peak voltage of 2 V, while the carrier wave has a frequency of 2 MHz and a peak voltage of 10 V.

Modulation Index Formula
The modulation index (m) is calculated using the following formula:
m = (Vm / Vc),
where Vm is the peak voltage of the message signal and Vc is the peak voltage of the carrier wave.

Step 1: Convert Frequencies to Hz
Since the given carrier wave frequency is in MHz and the message signal frequency is in kHz, we need to convert both frequencies to Hz for accurate calculations.
Carrier wave frequency = 2 MHz = 2 × 10^6 Hz
Message signal frequency = 5 kHz = 5 × 10^3 Hz

Step 2: Calculate the Modulation Index
Using the formula, we can calculate the modulation index as follows:
Vm = 2 V (given)
Vc = 10 V (given)
m = (2 V / 10 V)
m = 0.2

Final Answer
Therefore, the modulation index is 0.2, which corresponds to option B.
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A message of frequency 5 kHz and peak voltage of 2 V is used to modulate a carrier wave of frequency 2 MHz and a peak voltage of 10 V. The modulation index is​a)0.01b)0.2c)0.1d)1Correct answer is option 'B'. Can you explain this answer?
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