Power (physics)
Power is the rate of energy transfer per unit time.
Power is a fundamental physical quantity defined as the rate at which energy is transferred or converted per unit time. In the International System of Units, its unit is the watt (W), equal to one joule per second. Power is a scalar quantity and is central to understanding mechanical, electrical, and thermal systems. In older scientific works, power was sometimes referred to as activity. Its dimension is energy divided by time, and while the watt is the standard SI unit, other common measures include horsepower (one mechanical horsepower equaling about 745.7 watts), ergs per second, foot-pounds per minute, dBm (a logarithmic measure relative to one milliwatt), calories per hour, BTU per hour, and tons of refrigeration.
Power can be understood as the time derivative of work or, more generally, of total mechanical energy (the sum of kinetic and potential energy). For a force acting on a body moving at a given velocity, the mechanical power generated equals the product of that force and the velocity. In rotational systems, power is the product of torque and angular velocity. In fluid power systems, such as hydraulic actuators, power is given by pressure multiplied by volumetric flow rate. In electrical circuits, instantaneous power delivered to a component is the product of the voltage across it and the current through it; for a resistor with a constant voltage-to-current ratio, power can also be expressed as the square of the current times resistance.
Average power over a time interval is the total work performed divided by that interval, while instantaneous power is the limiting value of average power as the time interval approaches zero. In a lossless mechanical system, input power must equal output power, which yields a simple formula for mechanical advantage based on the ratio of input to output velocities (or, in rotating systems, angular velocities). This principle defines the maximum performance of a device in terms of velocity ratios determined by its physical dimensions, such as gear ratios.
- SI unit
- watt (W)
- Definition
- rate of energy transfer or conversion per unit time
- Dimension
- energy divided by time
- Common units
- horsepower (hp), ergs per second, foot-pounds per minute, dBm, calories per hour, BTU per hour, tons of refrigeration
- Mechanical power formula
- product of force and velocity, or torque and angular velocity
- Electrical power formula
- product of current and voltage
Quick Facts
- Unit
- watt (W)
- Symbols
- P
- Baseunits
- kg⋅m2⋅s−3
- Dimension
- wikidata
Facts from the source article.
Lore & Background
Power is a scalar quantity representing the rate at which energy is transferred or converted over time. In the International System of Units, its unit is the watt, equivalent to one joule per second. The concept is defined as the time derivative of total mechanical energy—the sum of kinetic and potential energy—or, in cases where only work is considered, as the time derivative of work. A key characteristic is that mechanical power generated by a force acting on a body moving at a given velocity is expressed as the product of that force and the velocity. If the force is constant over a distance, work is the product of force and displacement, and power simplifies to force times velocity. For variable forces along a curved path, work is defined by a line integral, but the instantaneous power formula remains valid via the fundamental theorem of calculus. In older texts, power was sometimes called activity. The dimension of power is energy divided by time, and common units include the watt, horsepower (one mechanical horsepower equals about 745.7 watts), ergs per second, foot-pounds per minute, dBm, calories per hour, BTU per hour, and tons of refrigeration. Average power over a period is the total work divided by the time interval, while instantaneous power is the limit of average power as the time interval approaches zero. In mechanical systems, power is the product of force and velocity or, for rotating shafts, the product of torque and angular velocity. In fluid power systems, it is the product of pressure and volumetric flow rate. For electrical components, instantaneous power is the product of voltage across the component and current through it; for a resistor with constant voltage-to-current ratio, power also equals the current squared times resistance. In lossless mechanical systems, input power equals output power, providing a simple relationship for mechanical advantage based on velocity or torque ratios.
Reader's Guide
The concept of power distinguishes between energy quantity and energy delivery rate. For example, burning one kilogram of coal releases more energy than detonating a kilogram of TNT, but the TNT reaction delivers more power because it releases energy more quickly. Average power over a time interval Δt is ΔW/Δt, while instantaneous power is the limit as Δt approaches zero. When power is constant, work equals power multiplied by time. In older works, power is sometimes called activity. Understanding power is essential for analyzing engines, electrical circuits, and any system involving energy conversion.
Did You Know?
- The unit of power in the International System of Units is the watt (W), equal to one joule per second.
- The output power of a motor is the product of torque and angular velocity.
- In older works, power is sometimes called activity.
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