A sinusoidal carrier voltage is amplitude modulated.The resultant amplitude modulated wave has maximum and minimum amplitude of `120V` and `80V` respectively.The amplitude of each sideband is:

Options

A. `10V`
B. `5V`
C. `20V`
D. `15V`

Answer

To solve the problem of finding the amplitude of each sideband in an amplitude modulated (AM) wave, we can follow these steps:

### Step 1: Understand the given information
We are given:
- Maximum amplitude of the AM wave, \( A_{max} = 120V \)
- Minimum amplitude of the AM wave, \( A_{min} = 80V \)

### Step 2: Set up the equations
In amplitude modulation, the maximum and minimum amplitudes can be expressed in terms of the carrier amplitude (\( A_c \)) and the modulation amplitude (\( A_m \)):
1. \( A_{max} = A_c + A_m \) (Equation 1)
2. \( A_{min} = A_c - A_m \) (Equation 2)

### Step 3: Substitute the known values
From the given values:
1. \( 120 = A_c + A_m \) (from Equation 1)
2. \( 80 = A_c - A_m \) (from Equation 2)

### Step 4: Solve the equations
Add both equations:
\[ (120) + (80) = (A_c + A_m) + (A_c - A_m) \]
This simplifies to:
\[ 200 = 2A_c \implies A_c = \frac{200}{2} = 100V \]

Now, substitute \( A_c \) back into either equation to find \( A_m \). Using Equation 1:
\[ 120 = 100 + A_m \implies A_m = 120 - 100 = 20V \]

### Step 5: Calculate the amplitude of each sideband
The amplitude of each sideband (\( A_{sb} \)) in amplitude modulation is given by:
\[ A_{sb} = \frac{A_m}{2} \]
Substituting the value of \( A_m \):
\[ A_{sb} = \frac{20}{2} = 10V \]

### Conclusion
The amplitude of each sideband is \( 10V \).