A Note on the Experimental Measurement of the High-Frequency Resistance of Wires
John Ambrose Fleming · Proceedings of the Physical Society of London · 1910
The Author refers to a Paper read by him in December, 1909, before the Institution of Electrical Engineers on Quantitative Measurements in Connection with Radio-Telegraphy" (" Journal," Inst. Elec. Eng., Vol. XLIV., p. 349, 1910), in which he described an apparatus consisting of a differential air thermometer having tubular bulbs into which similar wires could be placed, and by means of which a comparison could be made of the high-frequency (H.F.) resistance R' of a straight wire and its steady or ohmic resistance R. If two equal wires have passed through one, a steady current A and through the other a H.F. current A 1 , then if these currents are adjusted until the rate of heat evolution in each case is the same we have A 2 R = A 1 2 R'. Certain precautions are described in the Paper for eliminating in-equalities, but by means of correct reading H.F. ammeters as devised by the Author, the ratio of the resistances R'/R can be determined from the ratio of the mean square currents A 2 /A 1 2 . The H.F. currents used were obtained by condenser discharges and the equiheating steady current determined by means of the differential thermometer arrangement having two equal wires in the two tubular bulbs. It is then shown that the results for straight wires agree very well with the formulæ given by Lord Kelvin and by Dr. A. Russell for the ratio R'/R for wires of different sizes and for different frequency. It is pointed out that the correction to be applied for damped oscillations as compared with persistent oscillations is at most 1 per cent. in the cases measured and that the correction for the heating effect of the condenser charging current is negligible. The case of spiral wires is then discussed. The resistance Rdouble prime of a spiral is greater than that of the same wire R' stretched out straight. In the cases examined the ratio Rdouble prime/R exceeds R'/R by about 50 to 80 per cent. A formula given by Dr. Nicholson for Rdouble prime/R is then discussed, and it is shown that it does not agree with the results of observation. Experiments are also described on the H.F. resistance of wires of magnetic metals, and it is shown that in this case the observed value of R'/R can be used to determine the permeability for small H.F. magnetising forces.