Power & Efficiency Reference Cheat Sheet

Key Facts

• Power is the rate of energy transfer and is calculated with $P = \frac{E}{t}$, where $P$ is in watts, $E$ is in joules, and $t$ is in seconds.
• Mechanical power can be calculated from work using $P = \frac{W}{t}$ because work is an energy transfer.
• When a constant force acts in the direction of motion, mechanical power can be calculated with $P = Fv$.
• Electrical power can be calculated with $P = IV$, where $I$ is current in amperes and $V$ is potential difference in volts.
• Using Ohm's law, electrical power can also be written as $P = I^2R$ or $P = \frac{V^2}{R}$.
• Efficiency is calculated with $\eta = \frac{E_{\text{useful}}}{E_{\text{input}}} \times 100\%$ or $\eta = \frac{P_{\text{useful}}}{P_{\text{input}}} \times 100\%$.
• No real machine is $100\%$ efficient because some input energy is always transferred to unwanted forms such as thermal energy or sound.
• One watt is one joule per second, so $1\,\text{W} = 1\,\text{J/s}$.

Vocabulary

Power

Power is the rate at which energy is transferred or work is done.

Watt

A watt is the SI unit of power and equals one joule of energy transferred per second.

Efficiency

Efficiency is the fraction or percentage of input energy or power that becomes useful output.

Useful Output

Useful output is the part of the transferred energy or power that accomplishes the intended task.

Wasted Energy

Wasted energy is energy transferred to forms that are not useful for the intended purpose, such as heat or sound.

Electrical Power

Electrical power is the rate at which electrical energy is transferred by a circuit component.