Stored energy and coil combinations

Stored magnetic energy

A coil through which a current i flows stores energy in magnetic form, rather than as heat as a resistor does through the Joule effect. This energy is given by:

E = (1/2) * L * i^2 (expressed in joules)

This energy is returned to the circuit when the current decreases: the coil is a reactive component; on average, it does not consume energy, but stores it and then returns it.

Series connection

For two coils with no magnetic coupling (no mutual inductance) connected in series, the equivalent inductance is the sum of the individual inductances, as with resistors:

L_eq = L1 + L2

Parallel connection

For a parallel connection, a law analogous to that for resistors in parallel applies:

1/L_eq = 1/L1 + 1/L2

Example

L1	L2	Series	Parallel
10 mH	20 mH	30 mH	approximately 6.7 mH

Common pitfall

These formulas assume there is no magnetic coupling between the coils. If they are close together and share part of their flux (mutual inductance M), the equation becomes L_eq = L1 + L2 ± 2*M, depending on the direction of the windings. Another common pitfall is confusing the energy formulas for the coil (E = 1/2 * L * i^2) and the capacitor (E = 1/2 * C * u^2).