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THE ABSOLUTE MEASUREMENT OF INDUCTANCE."

By Edward B. Rosa and FREDERICK W. GROVER.

1. METHODS OF MEASURING INDUCTANCE.

Self inductance may be determined in absolute measure (that is, in terms of resistance and time) by the methods of Maxwell, Wien, or Rowland. The first named is complicated and scarcely capable of giving results of high accuracy. The other two methods are probably capable of yielding results of satisfactory accuracy, but so far as we know few results by these methods have been published, and none of a degree of accuracy equal to the results which have been obtained in the absolute measurement of a capacity.

The most obvious method of directly determining the inductance of a coil, originally proposed by Joubert, consists in first determining the impedance of the coil and then calculating the inductance, after having found the ohmic resistance of the wire and the frequency of the current employed.

Brew has given some determinations of inductance by this method, using a Cardew voltmeter, first in series with the inductive coil and second with the coil cut out. Knowing the resistance of the coil and of the instrument, and the frequency of the current, the inductance is calculated. The results on a single coil are given; they show considerable variations, as would be expected. Nothing is said of the wave form, although the formula employed presupposes a sine wave.

Several variations of this method are described by Gray and Fleming. According to Gray, a noninductive resistance is placed in series with the coil whose inductance is to be measured, and an alternating current passed through both. By means of an electrometer,

a A paper presented at the International Electrical Congress, St. Louis, 1904. b Electrician: 25, p. 206; 1890. c Absolute measurements: II, pt. II, p. 488. d Handbook for the Electrical Laboratory: Vol II, p. 205.

the differences of potential at the terminals of the noninductive resistance R,, and of the inductive coil (resistance R, and inductance L) are measured. The inductance is then given by the expression

2

R/R,
L=

V

R p being 27 times the frequency of the current employed, which is to be as nearly simply harmonic as possible.

According to Fleming, we “first send through the coil a continuous current and observe the potential difference of the ends of the coil with an electrostatic voltmeter, and measure the current flowing through it. Then repeat the experiment, using the alternating e. m. f. The ammeter should be a Kelvin balance, or dynamometer, or hot wire ammeter, suitable for both continuous and alternating currents. Adjust the voltage so that the current is the same in both cases.

Then if A is this current, and if V is the volt-fall down the coil with continuous current, and V' that with the alternating current, and if R is the resistance and L the inductance of the coil, we have

A

R

A'=

✓R" +p’L where p = 2n times the frequency of the alternating current.” Therefore,

R

V2
L=

V2

V12

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or the volt-drop may be kept constant and the current measured in
each case.
Then

R
L=

P

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If the current is not of sine wave form, a correction must be applied.

2. THE METHOD OF THIS PAPER.

It occurred to us that a modification of the method quoted above from Gray would be as well adapted to precision measurements as any other proposed. Instead of using the electrometer to measure the difference of potential at the terminals of the inductive coil and of a fixed resistance R, we vary the resistance R until the difference of potential at its terminals is equal to that at the terminals of the

inductive coil, as shown by an electrometer. Then, since the alternating current I is the same in both, and a sine wave form is assumed,

IR=1/+pI,

r being the ohmic resistance of the inductive coil. Then

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FIG. 1.- A B=noninductive resistance; B (D--impedance triangle for inductive coil.

This is an extremely simple formula, in which only two quantities, the resistance and the frequency, have to be determined accurately. The resistance r is usually so small that an approximate value for it is sufficient. In the simplicity and directness of the method and the small number of quantities to be determined lie the advantages of this over other methods.

The chief objection to this method is that it is necessary to have a perfect sine current, or to know the exact form of the current wave in order to calculate the correction due to any harmonics that may be present. So far as we know no accurate determination of inductance by this method has ever been published, and probably because of this requirement. Most alternating current generators yield currents having harmonics of considerable magnitude, and the wave form of course varies according to the load. It is necessary, therefore, to determine the wave form of the particular current used in the experiment in order to obtain the proper correction factor.

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