Power
The standard unit for measuring electrical power is the Watt, which is equal to 1 Joule/second. In the context of electricity, power is often used to describe either an electrical device or a generation system. In the first case, the power rating of a device gives its instantaneous electrical demand. For instance, in order to remain lit, a 10-Watt compact fluorescent light bulb would continuously require 10 Watts of electrical power. In the second case, the power rating of a generation system describes its capacity. For example, a 200-Watt photovoltaic module is capable of producing 200 Watts of electrical power when in peak sun conditions. Power is a conserved quantity, meaning that the amount of electrical power provided to a circuit (for instance, by a battery or a photovoltaic module) is equal to the amount of power dissipated (or used) in the circuit by resistors or devices.
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Though the terms are often used interchangeably in everyday speech, energy and power are two different things. Power is the rate at which energy is transferred, used or transformed. When lit, a 100-Watt incandescent light bulb is continuously converting 100 Watts of electrical power into light and heat. As already discussed, energy is the ability to do work, but it can also be quantified as the amount of power consumed or generated over a period of time. The unit Watt is equivalent to one joule of energy per second. That 100-Watt light bulb will transform 100 Watt-hours or 360 kilojoules of electrical energy into thermal and electromagnetic energy every hour that it is lit. Therefore, if power is not changing over time, the relationship between energy and power can be explicitly described by the equation:
Energy = Power x Time
If power varies as a function of time, then energy is the integral of power with respect to time:
In other words, Energy (or "Work") (W) is equal to the integration of power (P) over a specified time interval.
The power equation describes the relationship between voltage, current and power. Recalling that power is the amount of energy transformed or transferred per second, it then makes sense that that power would be the amount of energy per unit of charge multiped the amount of charge that is passing per second. Therefore, power is equal to the product of voltage and current.
Other Mathematical Relationships
Mathematically, power can also be described by the following relationships by manipulating the power equation and Ohm's Law:
P = IV = I2R = V2/R
Where
P: Power
I: Current
V: Voltage
R: Resistance
