Which equation represents efficiency of power?

The equation representing the efficiency of power is defined as the ratio of the useful output power to the input power. This reflects how effectively a system converts input energy into useful work.

In this context, power is often thought of in terms of how much energy is produced (p_out, or output power) versus how much energy is consumed (p_in, or input power). Therefore, the equation for efficiency as the ratio of output power to input power shows how well a system is performing relative to its energy consumption.

This ratio provides a percentage that helps to evaluate the performance of machines and systems, allowing for comparisons across different devices or processes. High efficiency indicates that a large portion of the input power is being converted to useful output power, while low efficiency implies significant energy losses, likely due to friction, heat, or other factors.

The other options, while related to concepts of work and mechanical effort, either misrepresent the relationship between input and output power or do not pertain directly to the definition of efficiency in terms of power systems. The correct option effectively captures the essence of measuring efficiency in energy and power contexts.