How is decibels (dB) calculated for power?

The calculation of decibels (dB) for power is based on a logarithmic scale that represents the ratio of two power levels. The correct formula for calculating decibels when dealing with power is dB = 10 log10(P1/P2). This formula is used because the decibel scale is a logarithmic measure of the ratio of a physical quantity, specifically power in this case.

The reason the correct formula involves a factor of 10 and the logarithm is that decibels express a ratio rather than an absolute value, to facilitate easier comparison of power levels that can span large numbers. The logarithmic nature compresses the range of potential values, making them more manageable and understandable.

In context, when you see options involving a factor of 20, those are typically used for voltage or pressure measurements, where the relationship between power and voltage is squared (P ∝ V²). Therefore, when measuring voltages or pressures, the formula becomes dB = 20 log10(V1/V2) because voltage is a linear factor related to power.

The incorrect answer provided (C), uses a formula that is appropriate for calculating the ratio in a way that does not correspond to how decibels should be calculated for