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# Inductance

Author: E.E. Kimberly

As described on page 4 and shown in Fig. 1-5, a current in a conductor produces a magnetic field around that conductor. When the current is increased or decreased, the strength of the magnetic field also increases or decreases. Any change in the field strength causes an emf to be generated or induced in the conductor. This phenomenon is called self-induction. The emf of self-induction is always in such a direction along the conductor as to oppose the change in current which causes the change in field strength that produces the emf. Thus, if the current decreases, the induced emf tends to prevent the decrease.

The emf of self-induction is proportional to the rate of change of field strength. The field strength produced by a current in a conductor with no iron in its magnetic field is proportional to the current. If the conductor is formed into a coil of N turns which are so located that all the flux produced by the current in every turn cuts every turn, then the emf generated in each turn would be N times as great as if any turn were cut by only the flux produced by the current in that turn. The flux produced by the current in every turn generates an emf in every other turn also. In a coil, the entire inductance phenomenon within the coil produced by the current of the coil is called the self-inductance, or merely the inductance, of the coil. Such inductance is denoted by L.

As stated on page 2, if a magnetic flux through a coil changes magnitude at a rate of 108 flux linkages per second, 1 volt is generated in the coil. If the flux through the coil is produced by current in the coil and that current is changing at a rate of 1 ampere per second when an electromotive force of 1 volt is generated, the coil is said to have an inductance of 1 henry. This relation may be stated in equation form as follows:

(5-1)

where L is the inductance, in henrys; θ is the flux, in maxwells; I is the current, in amperes; and N is the number of turns in the coil. The constant 108 converts maxwells of the cgs system to the practical system of volts and amperes.

Example 5-1. - A coil is wound with 1000 turns. When a current of 4 amperes is passed through the coil, a flux of 3,000,000 maxwells is produced, (a) How many flux linkages are there in the coil? (6) What is the inductance L1 in henrys? (c) If the number of turns is reduced to 500 and the current is kept the same as before, what is the new inductance L2?

Solution. - (a) The number of flux linkages is

(6) The inductance is

(c) The new flux is

The corresponding number of flux linkages is and the inductance is

It should be noted that in the example the inductances were proportional to the squares of the numbers of turns in the coil. With constant current the flux is proportional to the number of turns; and, when the number of turns is reduced to half of the original number, the flux is also reduced to half its original value. Therefore, the flux linkages per ampere are proportional to the squares of the numbers of turns in the coil. This is an idealized case in which it is assumed that the coil does not change size or shape when the number of turns is changed and that the ability of the flux path material to carry flux does not change as the flux density changes. Refinements of these calculations which apply to more practical cases of coils having various ratios of core diameter, length, and coil diameter may be found in a Bulletin of the U.S. Bureau of Standards designated as Reprint 169.

Last Update: 2010-10-06