Question:
In amplitude modulation, if the amplitude of the message signal is increased by \(20\%\) and the amplitude of the carrier wave is decreased by \(20\%\), then the percentage increase in the modulation index is
In amplitude modulation, if the amplitude of the message signal is increased by \(20\%\) and the amplitude of the carrier wave is decreased by \(20\%\), then the percentage increase in the modulation index is
Show Hint
The modulation index in AM is
\[
\boxed{
m=\frac{A_m}{A_c}.
}
\]
Any percentage change in \(A_m\) or \(A_c\) directly changes the modulation index according to this ratio.
Updated On: Jul 18, 2026
- \(75\)
- \(40\)
- \(25\)
- \(50\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Recall the expression for modulation index.
For amplitude modulation,
\[
m=\frac{A_m}{A_c},
\]
where
\[
A_m
\]
is the amplitude of the message signal and
\[
A_c
\]
is the amplitude of the carrier wave.
Step 2: Find the new modulation index. The message amplitude is increased by \(20\%\), so \[ A_m'=1.2A_m. \] The carrier amplitude is decreased by \(20\%\), so \[ A_c'=0.8A_c. \] Hence, \[ m' = \frac{A_m'}{A_c'} = \frac{1.2A_m}{0.8A_c} = 1.5m. \]
Step 3: Calculate the percentage increase. The increase in modulation index is \[ 1.5m-m=0.5m. \] Therefore, \[ \text{Percentage increase} = \frac{0.5m}{m}\times100 = 50\%. \] Hence, \[ \boxed{50\%.} \] Therefore, the correct option is \(\boxed{(D)}\).
Step 2: Find the new modulation index. The message amplitude is increased by \(20\%\), so \[ A_m'=1.2A_m. \] The carrier amplitude is decreased by \(20\%\), so \[ A_c'=0.8A_c. \] Hence, \[ m' = \frac{A_m'}{A_c'} = \frac{1.2A_m}{0.8A_c} = 1.5m. \]
Step 3: Calculate the percentage increase. The increase in modulation index is \[ 1.5m-m=0.5m. \] Therefore, \[ \text{Percentage increase} = \frac{0.5m}{m}\times100 = 50\%. \] Hence, \[ \boxed{50\%.} \] Therefore, the correct option is \(\boxed{(D)}\).
Was this answer helpful?
0
0
Top TS EAMCET Physics Questions
- A wooden box lying at rest on an inclined surface of a wet wood is held at static equilibrium by a constant force $F$ applied perpendicular to the incline. If the mass of the box is $1\,kg$, the angle of inclination is $30^{\circ}$ and the coefficient of static friction between the box and the inclined plane is $0.2$, the minimum magnitude of $\vec{F}$ is (Use $ g = 10\,m/s^2$)
- A metre scale made of steel reads accurately at $25^{\circ} C$ . Suppose in an experiment an accuracy of $0.06\, mm$ in $1\,m$ is required, the range of temperature in which the experiment can be performed with this metre scale is (coefficient of linear expansion of steel is $ 11 \times 10^{-6} /^{\circ} \, C$ )
- Consider a solenoid carrying current supplied by a DC source with a constant emf containing iron core inside it. When the core is pulled out of the solenoid, the change in current will
- A parallel beam of light of intensity \(I_0\) is incident on a coated glass plate. If \(25\%\) of the incident light is reflected from the upper surface and \(50\%\) of light is reflected from the lower surface of the glass plate, the ratio of maximum to minimum intensity in the interference region of the reflected light is
- A thermocol box has a total wall area (including the lid) of $1.0 m ^{2}$ and wall thickness of $3 cm$. It is filled with ice at $0^{\circ} C$. If the average temperature outside the box is $30^{\circ} C$ throughout the day, the amount of ice that melts in one day is [Use $K_{\text {thermocol }}=0.03 W / mK$ $.L_{\text {fusion (ice) }}=3.00 \times 10^{5} J / kg ]$
View More Questions
Top TS EAMCET Modern Physics Questions
- For any fixed distance, the electromagnetic force between two protons is \( 10^n \) times of the gravitational force between them. Then \( n = \)
- Photons of energy 4.5 eV are incident on a photosensitive material of work function 3 eV. The de Broglie wavelength associated with the photoelectrons emitted with maximum kinetic energy is nearly
- If the difference in the frequencies of the first and second lines of Lyman series of hydrogen atom is f, then the difference in frequencies of the first and second lines of Balmer series of hydrogen atom is
- When electromagnetic radiation of wavelength 310 nm falls on the surface of a metal having work function 3.55 eV, the velocity of photoelectrons emitted is \( x \times 10^5 \text{ms}^{-1} \). The value of \( x \) is (Nearest integer) (\( m_e = 9 \times 10^{-31} \text{kg} \))
- Bose-Einstein statistics is applicable to particles with
View More Questions
Top TS EAMCET Questions
- A bag contains $5$ red balls, $3$ black balls and $4$ white balls are drawn at random. The probability that they are not of same colour is
- If $cosec\, \theta - \cot \theta = 2017$, then quadrant in which $\theta $ lies is
- If $a$ is a unit vector, then $| a \times \hat{ i }|^{2}+| a \times \hat{ j }|^{2}+| a \times \hat{ k }|^{2}=$
- $A$ straight line makes an intercept on the $Y$-axis twice as long as that on $X$-axis and is at a unit distance from the origin. Then the line is represented by the equations
- Let $S$ and $S'$ be the foci of an ellipse and B be one end of its minor axis. If $SBS'$ is an isosceles right angled triangle then the eccentricity of the ellipse is
View More Questions