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Power and efficiency

Power is how quickly energy is transferred or work is done, measured in watts. A machine's efficiency is the ratio of useful power out to input power, and is always less than 1 because some energy always turns into heat along the way.

P = \dfrac{W}{t}

power, work per time

P = Fv

power at constant speed

\eta = \dfrac{P_{out}}{P_{in}}

efficiency

Symbols

$P$	power	W
$\eta$	efficiency
$t$	time	s

Example

A motor has $\eta = 0.80$ and delivers $2.0$ kW of useful power. The input power is $P_{in} = P_{out}/\eta = 2.0/0.80 = 2.5$ kW.

Input power is always larger than useful power – divide useful power by

\eta

, not the other way around.

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Part of Foundations of Physics: Work, energy and power.