What is the formula for a decibel of power?

The correct formula for measuring the decibel (dB) level of power is indeed expressed as 10 log(P/P0), where P is the power level being measured and P0 is the reference power level.

This formula is derived from the logarithmic nature of decibels, which are a dimensionless unit used to express ratios. In the case of power, the logarithmic scale helps to simplify the representation of large ranges of power levels that can occur in various electrical systems.

The factor of 10 in the formula is crucial because it originates from the definition of the decibel itself, which is one-tenth of a Bel. This means that when you take the logarithm of a power ratio and multiply it by 10, you convert that power ratio into decibels.

In contrast, the options involving voltage use a different formula because the power in an electrical system is proportional to the square of the voltage (P ∝ V^2). Therefore, when dealing with voltage ratios, the formula uses a factor of 20 instead of 10, resulting in 20 log(V/V0) for voltage comparisons.

Thus, while both power and voltage measurements can be expressed in decibels, they require different formulas