Electric Power
Electric Power is the amount of power that is used within an electric circuit, expressed as P, and generally measured in watts (W). In simple terms, it is the rate at which electrical energy is used or transffered.
In essence, you can consider electric power as the amount of work being performed by electricity every second within a given circuit.
In practice, the Electric Power, P, in any given part of a circuit is equal to the voltage (V) multiplied by the current (I) across that part of the circuit.
The Water Analogy of Electric Power
A common way that electricity — and electric power — can be described to better visualize how it works, is to use water as an analogy.
Imagine we have water flowing at some rate through a hose. In this circumstance:
- Voltage (V) — is the water pressure. The amount of pressure that is being built up before the water enters the hose, and then forced through the hose. In electrical circuits, this is generally done with a power source, like a battery or turbine.
- Current (I) — is the flow rate. The literal amount of water molecules that are passing through a given cross-section of the hose per second. In electricity, this is the flow of electrons, rather than water molecules.
- Power (P) — is the total energy of the water used to do work. With water, this can be converted into electricity in a dam or water wheel, or applied as kinetic energy in the form of a power washer to clean something. In electronics, that total energy is used to power devices.
The exact amount of power in electrical devices needs to be controlled precisely. We don’t want too much power, because you’ll burn components. To little, and the light-bulb won’t shine brightly enough. To increase electrical power, we need to increase either the current, voltage or both.
The Generalized Power Law
Mathematically, this relationship between power, voltage, and current gives us what is known as the Generalized Power Law, also called Watt’s Law or the Power Law (not to be confused with the Power Law of Calculus or any number of “power law” in physics).
The Generalized Power Law for calculating electric power is given as
\begin{equation} P = VI \end{equation}
Where P is measured in watts (W), the voltage / potential difference V is measured in volts (V), and the current I is measured in amps (A). We can rearrange the above expression and solve for power, voltage, or current, depending on what we need.
\[ P = VI \quad V = \frac{P}{I} \quad I = \frac{P}{V} \]
Ohm’s Law Substitution Into The Generalized Power Law
We can further extend the Generalized Power Law by substituting Ohm’s Law into it, thereby adapting it with algebra to calculate electric power from different quantity terms.
Ohm’s Law solves for current as I=V/R — current is equal to voltage divided by resistance. If we are solving for electric power with the Power Law, and do not have a value for current, then we can substitute Ohm’s Law in place of the term for current, I, as follows
\[ P = VI = V \Big( \frac{V}{R} \Big) = \frac{V^2}{R} \]
If we have current and resistance, but don’t have voltage, then we can manipulate Ohm’s Law to solve for voltage (V=IR) which we then substitute into the Power Law giving us
\[ P = (IR)I = I^2 R \]
Power vs Energy
Electrical Power and Electrical Energy are related, but not technically the same.
- Power (Watts) — Power is measured in a unit called Watts, which is how much energy you are using right now, at this moment. Exactly how much energy that is being pulled by your device each second.
- Energy (Watt-hours) — is the total electrical energy used over time. It is not always relevant how much power is used by a light-bulb or space heater each second. It is more important to know the energy drawn over 8 hours of usage, or over a month (especially for your electric bill).
Units of Electric Power
As stated above, the units of electric power are are measured in watts (W). It is also useful to look at how these units are derived. This is equivalent to Current (Amperes) times Voltage (Volts, hence $P=VI$).
There are many different units for power, since there are many different types of power. In this case, we define power as electric power using the power law (P=VI). If we write this formula without any of the quantities, just the units, we can see that in this case watts are equal to voltage times amperes:
\[ W = V \cdot A \]
