ARRL Technician Practice Exam

What is the approximate amount of change, measured in decibels (dB), for a power increase from 20 watts to 200 watts?

1. 5 dB

2. 10 dB

3. 15 dB

4. 20 dB

The correct answer is: 10 dB

To calculate the change in power in decibels (dB) when increasing power, you can use the formula: \[ \text{dB} = 10 \times \log_{10}\left(\frac{P_2}{P_1}\right) \] In this case, \( P_1 \) is 20 watts and \( P_2 \) is 200 watts. To find the ratio of the two power levels, divide 200 watts by 20 watts: \[ \frac{P_2}{P_1} = \frac{200 \text{ watts}}{20 \text{ watts}} = 10 \] Now, substitute this ratio back into the formula: \[ \text{dB} = 10 \times \log_{10}(10) \] Since \( \log_{10}(10) = 1 \), the calculation simplifies to: \[ \text{dB} = 10 \times 1 = 10 \text{ dB} \] This indicates that increasing the power from 20 watts to 200 watts results in an increase of approximately 10 dB. This principle is critical in understanding how decibel measurements relate to power changes