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 find the percentage modulation in a communication system where a message signal is modulated with a carrier signal, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Amplitudes**:
- The message signal is given as \( V_m = 20 \sin[2\pi(1500t)] \).
- The carrier signal is given as \( V_c = 80 \sin[2\pi(100000t)] \).
- From these equations, we can identify the amplitudes:
- Amplitude of the message signal \( A_m = 20 \).
- Amplitude of the carrier signal \( A_c = 80 \).

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

3. **Substitute the Values**:
- Substitute the values of \( A_m \) and \( A_c \) into the formula:
\[ \text{Percentage Modulation} = \left( \frac{20}{80} \right) \times 100 \]

4. **Calculate the Ratio**:
- Calculate \( \frac{20}{80} \):
\[ \frac{20}{80} = \frac{1}{4} = 0.25 \]

5. **Calculate the Percentage**:
- Now multiply by 100 to get the percentage:
\[ \text{Percentage Modulation} = 0.25 \times 100 = 25\% \]

### Final Answer:
The percentage modulation is **25%**.

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