Handbook of Electrical Engineering

482 HANDBOOK OF ELECTRICAL ENGINEERING

Figure 20.1 Mutually coupling and leakage fluxes in coils that share a common magnetic iron core.

is called the flux linkageψ. An emf is induced in the winding when the current is changed and

therefore when the flux linkage is changed in sympathy with the current. The emfeinduced is:-

e=

dψ

dt

=

dψ

dI

·

dI

dt

=L

dI

dt

(20.1)

which opposes the applied voltage at the terminals of the winding.

WhereLis the inductance of the winding in henrys (or flux linkages per ampere). IfIvaries
sinusoidally then the emf is induced in a co-sinusoidal manner,

e=L

d(Iˆsinωt)

dt

=ωLIˆcosωt volts

=XIˆcosωt

whereX=ωLis the inductive reactance at the frequencyω.

When the emf is induced in one winding by the current changing in a second winding the
process is called ‘induction by transformer action’ or ‘transformer induced emf’.

The rate of change of flux linkages can be brought about by rotating one winding with respect
to a second winding, as is the fundamental situation in a motor or generator. If the current that