ARRL Technician Practice Exam

What is the approximate change in decibels (dB) for a power increase from 5 watts to 10 watts?

1. 2 dB

2. 3 dB

3. 4 dB

4. 5 dB

The correct answer is: 3 dB

To determine the change in decibels (dB) for a power increase from 5 watts to 10 watts, you can use the formula for calculating decibels for power levels, which is: \[ \Delta \text{dB} = 10 \times \log_{10} \left( \frac{P_2}{P_1} \right) \] In this case, \( P_1 = 5 \) watts and \( P_2 = 10 \) watts. Plugging in these values gives: \[ \Delta \text{dB} = 10 \times \log_{10} \left( \frac{10}{5} \right) \] Calculating the fraction gives: \[ \frac{10}{5} = 2 \] Now, using the logarithm: \[ \log_{10}(2) \approx 0.301 \] Thus, we continue: \[ \Delta \text{dB} = 10 \times 0.301 = 3.01 \text{ dB} \] Rounding this value gives approximately 3 dB. A 3 dB increase signifies