A broadcast radio transmitter radiates 10 kW when the modulation percentage is 60. How much of this is carrier power?

Explanation

To find the carrier power of a broadcast radio transmitter that radiates 10 kW with a modulation percentage of 60%, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Transmitted power (PT) = 10 kW
- Modulation percentage = 60%

2. **Convert Modulation Percentage to Decimal**:
- Modulation percentage (μ) = 60% = 0.6

3. **Use the Formula for Carrier Power (PC)**:
- The relationship between carrier power (PC) and transmitted power (PT) is given by:
\[ PC = \frac{PT}{1 + \frac{\mu^2}{2}} \]

4. **Calculate μ²**:
- First, calculate μ²:
\[ \mu^2 = (0.6)^2 = 0.36 \]

5. **Substitute μ² into the Formula**:
- Now substitute μ² into the formula:
\[ PC = \frac{10 \text{ kW}}{1 + \frac{0.36}{2}} \]

6. **Calculate the Denominator**:
- Calculate \(\frac{0.36}{2}\):
\[ \frac{0.36}{2} = 0.18 \]
- Now add this to 1:
\[ 1 + 0.18 = 1.18 \]

7. **Calculate Carrier Power (PC)**:
- Now substitute back into the equation for PC:
\[ PC = \frac{10 \text{ kW}}{1.18} \approx 8.47 \text{ kW} \]

8. **Final Result**:
- The carrier power (PC) is approximately 8.47 kW.

### Final Answer:
The carrier power is approximately **8.47 kW**.