Variable Self-Inductance

There are electric circuits in which the self-inductance is not constant but in which it varies as a result of relative linear motion or rotary motion between portions of the magnetic circuit. Relays, solenoids, and some types of electric motors and generators are examples of variable self-inductance due to one member moving with respect to another.

When the self-inductance L is a variable Eq. 4-2 does not express the induced emf because it does not take into account the time variation of L. According to Eq. 4-6 the flux linkage is expressed in terms of self-inductance and the current by

[4-16]

A time variation of flux linkage inducing the voltage

[4-17]

Equation 4-17 shows that there are generally two components in the emf of self-induction. One of these is L di/dt and is due to the time variation in the current, and the other, i dL/dt, is due to the time variation of the self-inductance. It is important to note that emf can be induced in an inductive circuit even when the current is constant if the inductance undergoes a variation with time.