A message signal of peak voltage 20V is used to modulate a carrier wave of amplitude 40V in amplitude modulation. The ratio of maximum amplitude and minimum amplitude in amplitude modulated signal is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3 : 1
In amplitude modulation the amplitude of the carrier varies about its unmodulated value \( A_c \) by the message amplitude \( A_m \), so the modulated wave has maximum amplitude \( A_c + A_m \) and minimum amplitude \( A_c - A_m \).
\( A_{\max} = 40+20 = 60\,\mathrm{V},\qquad A_{\min} = 40-20 = 20\,\mathrm{V} \)
\( \displaystyle \frac{A_{\max}}{A_{\min}} = \frac{60}{20} = \frac{3}{1} \)
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 \( c(t) = A_c \sin\omega_c t \) represent carrier wave and \( m(t) = A_m \sin\omega_m t \) represent the message or the modulating signal … The modulated signal \( c_m(t) \) can be written as
\( \displaystyle c_m(t) = (A_c + A_m \sin\omega_m t)\sin\omega_c t = A_c\left(1 + \frac{A_m}{A_c}\sin\omega_m t\right)\sin\omega_c t \qquad (15.3) \)”