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Mutual Inductance and Transformers 14.1


The total magnetic flux linkage  in a linear inductor made of a coil is proportional to the current passing through it; that is,  ¼ Li (see Fig. 14-1). By Faraday’s law, the voltage across the inductor is equal to the time derivative of the total influx linkage; that is, v¼

d di ¼L dt dt

Fig. 14-1

The coefficient L, in H, is called the self-inductance of the coil. Two conductors from different circuits in close proximity to each other are magnetically coupled to a degree that depends upon the physical arrangement and the rates of change of the currents. This coupling is increased when one coil is wound over another. If, in addition, a soft-iron core provides a path for the magnetic flux, the coupling is maximized. (However, the presence of iron can introduce nonlinearity.) To find the voltage-current relation at the terminals of the two coupled coils shown in Fig. 14-2, we observe that the total magnetic flux linkage in each coil is produced by currents i1 and i2 and the mutual linkage effect between the two coils is symmetrical. 1 ¼ L1 i1 þ Mi2 2 ¼ Mi1 þ L2 i2 334 Copyright 2003, 1997, 1986, 1965 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.