In amplitude modulation determine the total maximum transmitted power, If the carrier output is 1 kW

Options

A. 1 kW
B. 0.5 kW
C. 1.5 kW
D. 2 kW

Answer

To determine the total maximum transmitted power in amplitude modulation when the carrier output is given as 1 kW, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Carrier power, \( P_c = 1 \, \text{kW} = 1000 \, \text{W} \)
- Modulation index, \( \mu = 100\% = 1 \)

2. **Use the Formula for Total Transmitted Power:**
The total transmitted power \( P_t \) in amplitude modulation is given by the formula:
\[ P_t = P_c \left(1 + \frac{\mu^2}{2}\right) \]

3. **Substitute the Values into the Formula:**
Substitute \( P_c \) and \( \mu \) into the formula:
\[ P_t = 1000 \, \text{W} \left(1 + \frac{1^2}{2}\right) \]

4. **Calculate the Modulation Index Contribution:**
Calculate \( \frac{\mu^2}{2} \):
\[ \frac{1^2}{2} = \frac{1}{2} = 0.5 \]

5. **Complete the Calculation:**
Now substitute back into the equation:
\[ P_t = 1000 \, \text{W} \left(1 + 0.5\right) = 1000 \, \text{W} \times 1.5 \]

6. **Final Calculation:**
\[ P_t = 1500 \, \text{W} = 1.5 \, \text{kW} \]

### Conclusion:
The total maximum transmitted power in amplitude modulation is \( 1.5 \, \text{kW} \).