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The significance of the sign of a mutual inductance

Published online by Cambridge University Press:  24 October 2008

R. R. Nimmo  and
H. D. Poole
R. R. Nimmo
Affiliation:
Clare College, Lecturer in Physics in the University of Western Australia
H. D. Poole
Affiliation:
Athelstan and Amy Saw Scholar of the University of Western Australia
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Extract

It is pointed out that there is some confusion concerning the meaning of the sign of a mutual inductance. The question is examined from first principles and it is shown that since the sign of a mutual inductance depends upon conventions as to sign of current directions, these, as well as the sign of the mutual inductance, must be given in order to specify what is really required—the relation between the directions of winding of the primary and secondary coils. It is also shown that in many cases it is possible to replace mutual inductance by a quantity which is numerically equal to the mutual inductance but which is independent of current directions. The two methods applied to a Wheatstone network yield consistent results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 4 , October 1932 , pp. 531 - 537
Copyright
Copyright © Cambridge Philosophical Society 1932

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References

* Cf. Jeans, J. H., Mathematical Theory of Electricity and Magnetism, 5th EditionGoogle Scholar; or Pidduck, F. B., A Treatise on Electricity, 2nd Edition.Google Scholar

† Cf. Dictionary of Applied Physics, Vol. II, Measurement of Inductance, p. 427; or Laws, F. A., Electrical Measurement, 1st Edition, p. 409.Google Scholar

‡ Cf. Gray, A., Absolute Measurements in Electricity and Magnetism, 2nd EditionGoogle Scholar; or Starling, S. G., Electricity and Magnetism, 5th Edition.Google Scholar

§ Cf. Hague, B., A.C. Bridge Methods, 2nd Edition (Pitman), p. 57Google Scholar, footnote.

∥ J. H. Jeans, loc. cit., p. 443.

* Dictionary of Applied Physics, Vol. II, Measurement of Inductance, p. 433.

* In the case in which L 12 = L 13 = 0 the directions of the currents can be so chosen that the transformation formulae have the same form in either current or winding sense mutual inductance operators. Where there are three mutual inductances as assumed above, this cannot be done and consequently this distinction between the current and winding sense mutual inductances cannot be overlooked. Cf. Hague, loc. cit., p. 59.

* Dictionary of Applied Physics, loc. cit., p. 431.

* Derivations of the balance conditions for this bridge appear to be unanimous in requiring that the current sense mutual inductance should be negative. This is the consequence of taking current directions which result in the current and winding sense mutual inductances having the same sign. Such a choice of current directions is very natural if cyclic currents are not used.

† Dictionary of Applied Physics, loc. cit., p. 427.

‡ Most statements of the balance conditions give the current sense mutual inductance as positive. As Maxwell's and Carey Foster's bridges are very similar from the analytical point of view, this is surprising.