# Alternating Current through pure inductors

by Kurokari
Tags: alternating, current, inductors, pure
 P: 4,663 It is useful also to look at the performance of a pure inductance using dc voltages and currents. If you apply a dc voltage V to a pure inductance L through a resistance R, you will build up a current I = V/R after some delay. This current through the inductance represents stored electrical energy in the form of magnetic field B. The stored energy EL is proportional to the magnetic field B squared times the stored volume. This is exactly analagous to a capacitor storing electrical energy in an electric field (capacitor). So in an inductance, to store energy in the magnetic field, the current must persist. The only way to do this is to short the inductance terminals together. Suprising but true. This is how the supercunducting magnets in MRI machines work. Read about persistent currents in http://en.wikipedia.org/wiki/Superconducting_magnet. When the terminals are shorted, the persistent current time constant is τ = L/R: $$I(t)=I_oe^{-Rt/L}$$ In superconducting magnets, R is like nano-ohms, so the persistence is very long.