ARRL Technician Practice Exam

What is the approximate change in decibels (dB) for a power decrease from 12 watts to 3 watts?

1. 3 dB

2. -3 dB

3. -6 dB

4. -9 dB

The correct answer is: -6 dB

To find the approximate change in decibels (dB) for a power decrease from 12 watts to 3 watts, you can use the formula for calculating the change in decibels due to a change in power: \[ \Delta dB = 10 \times \log_{10} \left( \frac{P2}{P1} \right) \] where \( P1 \) is the initial power level (12 watts) and \( P2 \) is the final power level (3 watts). Substituting the values gives: \[ \Delta dB = 10 \times \log_{10} \left( \frac{3}{12} \right) \] \[ \Delta dB = 10 \times \log_{10} \left( 0.25 \right) \] Calculating the logarithm: The logarithm of 0.25 is -0.602. Therefore, \[ \Delta dB = 10 \times (-0.602) = -6.02 \text{ dB} \] This value is approximately -6 dB. This indicates a decrease in power level, which is consistent with the concept that a decrease in power