Energy stored in an inductor

The Energy in an Inductor calculator computes the energy from the inductance and current.

INSTRUCTIONS: Choose units and enter the following:

• (L) Inductance
• (I) Current

Inductor's Energy (E_L): The energy is returned in Joules.  However, this can be  automatically converted to compatible units via the pull-down menu.

The Math / Science

The Inductor's Energy is found using  the following formula:  

`E_L = L/2I^2`

where:

• E_L = Inductor's Energy
• L = Inductance
• I = current

Inductors

Any current will create a magnetic field, so in fact every current-carrying wire in a circuit acts as an inductor! However, this type of “stray” inductance is typically negligible, just as we can usually ignore the stray resistance of our wires and only take into account the actual resistors. To store any appreciable amount of magnetic energy, one usually uses a coil of wire designed specifically to be an inductor.

All the loops' contribution to the magnetic field add together to make a stronger field. Unlike capacitors and resistors, practical inductors are easy to make by hand. One can for instance spool some wire around a short wooden dowel, put the spool inside a plastic aspirin bottle with the leads hanging out, and fill the bottle with epoxy to make the whole thing rugged. An inductor like this, in the form cylindrical coil of wire, is called a solenoid, c, and a stylized solenoid, d, is the symbol used to represent an inductor in a circuit regardless of its actual geometry.

How much energy does an inductor store? The energy density is proportional to the square of the magnetic field strength, which is in turn proportional to the current flowing through the coiled wire, so the energy stored in the inductor must be proportional to `I^2`. We write `L"/"2` for the constant of proportionality, giving

`E_L=L/2I^2`.

As in the definition of capacitance, we have a factor of 1/2, which is purely a matter of definition. The quantity L is called the inductance of the inductor, and we see that its units must be joules per ampere squared. This clumsy combination of units is more commonly abbreviated as the henry, 1 henry = 1 `J"/"A^2`. Rather than memorizing this definition, it makes more sense to derive it when needed from the definition of inductance. Many people know inductors simply as “coils,” or “chokes,” and will not understand you if you refer to an “inductor,” but they will still refer to `L` as the “inductance,” not the “coilance” or “chokeance!”

References

25.1 Capacitance and inductance by Benjamin Crowell, Light and Matter  licensed under the Creative Commons Attribution-ShareAlike license.