Glossary term
Power
The rate at which energy is transferred, converted, delivered, stored, or dissipated in a physical or engineered system.
Definition
quantityPower is the rate at which energy is transferred, converted, or dissipated per unit time.
Power is a fundamental quantity that connects energy to time across every engineering domain. In electrical systems it governs the design of generation, transmission, and consumption equipment. In mechanical systems it determines the output capacity of engines, motors, and actuators. In thermal systems it quantifies heat transfer rates. The distinction between active power, reactive power, and apparent power in AC systems is treated in dedicated entries.
Power is the time derivative of energy. If W is the energy transferred or converted up to time t, the instantaneous power is:
The SI unit of power is the watt (W), equal to one joule per second (\text{J/s}). Engineering systems span an enormous range: a microcontroller may consume milliwatts, a household appliance kilowatts, an industrial motor megawatts, a large power plant gigawatts. The non-SI unit horsepower (hp) remains common in mechanical engineering: 1 \, \text{hp} = 745.7 \, \text{W}.
Mechanical power
In mechanics, power is the rate at which a force does work. For a force F acting on a body moving at velocity v in the direction of the force:
For rotational systems, power is the product of torque T and angular velocity \omega:
This relation is central to the design and selection of engines, electric motors, gearboxes, pumps, and compressors. For a shaft rotating at n revolutions per minute:
The distinction between power and torque matters in practice: a high-torque, low-speed motor and a low-torque, high-speed motor can produce identical power, but their suitability depends on the load characteristics.
Electrical power in DC circuits
In a direct current (DC) circuit, instantaneous power delivered to a component is:
where V is the voltage across the component and I is the current through it. This product is the active power — the power that does useful work or is converted to heat. In AC circuits, the relationship between voltage, current, and power is more nuanced: instantaneous power fluctuates at twice the supply frequency, and the time-averaged active power depends on the phase angle between voltage and current. The concepts of reactive power, apparent power, and power factor, which arise specifically in AC systems, are treated in dedicated entries.
Engineering significance
Power is a primary design variable across virtually every engineering domain. In electrical power systems, generation capacity, transmission line ratings, and transformer ratings are expressed in power units. In mechanical design, the power demand of a machine drives the selection of prime movers and drive components. In electronics, power dissipation determines junction temperatures and reliability limits for semiconductors. In energy engineering, the relationship between installed power capacity, energy production, and load profiles governs grid stability and dispatch strategies.
Common mistakes
A common mistake is to mix instantaneous, average, peak, rated, and continuous power. A motor may tolerate short overloads that would be unacceptable as continuous duty, and an electronic component may survive pulsed dissipation only if junction temperature remains within limits. Another mistake is comparing power capacity with energy delivery: a 1 MW device can deliver very different total energy depending on operating time, duty cycle, storage, and availability. A good review states power type, averaging interval, duty cycle, thermal limit, measurement convention, and whether the value is input, output, or loss.