In communication system message signal is modulated with carrier signal given below
`V_in = 20 sin[2 pi (1500t)] `
`V_c = 80 sin[2pi (100000t)]` Find percentage modulation

Options

A. 0.15
B. 0.2
C. 0.25
D. 0.35

Answer

To solve the problem of finding the percentage modulation in a communication system where a message signal is modulated with a carrier signal, we can follow these steps:

### Step 1: Identify the Amplitudes of the Signals
The message signal \( V_m \) and the carrier signal \( V_c \) are given as:
- \( V_m = 20 \sin[2\pi(1500t)] \)
- \( V_c = 80 \sin[2\pi(100000t)] \)

From these equations, we can identify:
- The amplitude of the message signal \( A_m = 20 \)
- The amplitude of the carrier signal \( A_c = 80 \)

### Step 2: Use the Formula for Percentage Modulation
The formula for percentage modulation is given by:
\[ \text{Percentage Modulation} = \left( \frac{A_m}{A_c} \right) \times 100 \]

### Step 3: Substitute the Amplitudes into the Formula
Now, we can substitute the values we identified:
\[ \text{Percentage Modulation} = \left( \frac{20}{80} \right) \times 100 \]

### Step 4: Simplify the Calculation
Calculating the fraction:
\[ \frac{20}{80} = \frac{1}{4} = 0.25 \]
Now, multiplying by 100 to find the percentage:
\[ \text{Percentage Modulation} = 0.25 \times 100 = 25\% \]

### Step 5: Final Answer
Thus, the percentage modulation is:
\[ \text{Percentage Modulation} = 25\% \]