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Variable SelfInductance
There are electric circuits in which the selfinductance 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 selfinductance due to one member moving with respect to another. When the selfinductance L is a variable Eq. 42 does not express the induced emf because it does not take into account the time variation of L. According to Eq. 46 the flux linkage is expressed in terms of selfinductance and the current by
A time variation of flux linkage inducing the voltage
Equation 417 shows that there are generally two components in the emf of selfinduction. 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 selfinductance. 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.


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