A message signal of peak value 2 V is used to modulate a carrier wave of peak value 10 V. The modulation index of the amplitude modulated wave is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.2
In amplitude modulation the modulation index is the ratio of the peak value of the message signal to the peak value of the carrier wave.
\( \displaystyle \mu = \frac{A_m}{A_c} \)
\( A_m = 2\,\mathrm{V} \)
\( A_c = 10\,\mathrm{V} \)
\( \displaystyle \mu = \frac{2\,\mathrm{V}}{10\,\mathrm{V}} = 0.2 \)
The modulation index is kept below 1 to avoid distortion, and 0.2 satisfies this.
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Amplitude Modulation – “… Let c(t) = Ac sin ωct represent carrier wave and m(t) = Am sin ωmt represent the message or the modulating signal where ωm = 2πfm is the angular frequency of the message signal. … Here μ = Am/Ac is the modulation index; in practice, μ is kept ≤ 1 to avoid distortion.”