In an amplitude modulation, amplitude of carrier wave is 250mV and amplitude of message signal is 150mV. If `A_(MAX)/A_(MIN) = X/50` then find x...

Answer

To solve the problem, we need to find the value of \( x \) given the amplitudes of the carrier wave and the message signal in an amplitude modulation scenario.

### Step-by-Step Solution:

1. **Identify the given values**:
- Amplitude of the carrier wave, \( A_c = 250 \, \text{mV} \)
- Amplitude of the message signal, \( A_m = 150 \, \text{mV} \)

2. **Calculate the maximum amplitude \( A_{max} \)**:
\[ A_{max} = A_c + A_m = 250 \, \text{mV} + 150 \, \text{mV} = 400 \, \text{mV} \]

3. **Calculate the minimum amplitude \( A_{min} \)**:
\[ A_{min} = A_c - A_m = 250 \, \text{mV} - 150 \, \text{mV} = 100 \, \text{mV} \]

4. **Calculate the ratio \( \frac{A_{max}}{A_{min}} \)**:
\[ \frac{A_{max}}{A_{min}} = \frac{400 \, \text{mV}}{100 \, \text{mV}} = 4 \]

5. **Set up the equation based on the problem statement**:
According to the problem, we have:
\[ \frac{A_{max}}{A_{min}} = \frac{x}{50} \]
Substituting the value we found:
\[ 4 = \frac{x}{50} \]

6. **Solve for \( x \)**:
To find \( x \), multiply both sides of the equation by 50:
\[ x = 4 \times 50 = 200 \]

### Final Answer:
\[ x = 200 \]