The Behavior of Glass as a Dielectric in Alternating Current Circuits: II. The Effect of Frequency and of Temperature Upon the Power Loss

Abstract

Power factor, power loss per unit applied potential difference, and capacitance, for six glasses, at several constant temperatures, with frequency varying from 800 to 4000 cycles per sec. and for one glass with frequency varying from 100 to 1500 kilocycles per sec.; power factor of one glass at constant frequency of 1000 cycles per sec. with temperature varying from 30°C to 160°C and at -186°C.—Curves show $log\frac{P}{E^2}$, $logtan\phi$, and $logC$ respectively as functions of $logf$; $C$ as function of $Ctan\phi$ and $logtan\phi$ as function of temperature. For the audio frequency range, results fit equation $\frac{P}{E^2}=C\omega$ $tan\phi =\mathrm{const}\times f^n$ at all temperatures investigated; for the radio frequency range, $tan\phi$ is found to reach a minimum at about 700 kilocycles and to increase rapidly at higher frequencies; capacitance decreases with increasing frequency throughout the entire range. The exponent $n$ is found to decrease slightly with increase in temperature. At the constant frequency of 1000 cycles the variation of power factor with temperature for one glass fits the empirical equation, $tan\phi =0.0077T$. The results are compared with those of previous investigators. For the audio frequency range they are shown to accord with the von Schweidler equations and not to give the maximum value of $tan\phi$ to be expected from the theories of Wagner and Joffé. On the assumption that the exponent $n$ is to be identified with the exponent of the time factor in the equation for the absorption current, $i=\beta C_{0}E{t}^{-n}$, von Schweidler's equations are thrown into a form which permits the calculation of $n$, $\beta$, and $C_0$, the geometrical capacitance, from the variation of capacitance with frequency. Values of $n$, $\beta$ and $K_0$, the dielectric constant, so calculated are given. It is suggested that the rapid increase in power factor at frequencies above 700 kilocycles may indicate another cause of power loss effective only at higher frequencies. As a further test of Joffé's theory, values of the apparent parallel resistance of one condenser, calculated by extrapolation from power loss measurements for a frequency of one-sixtieth of a cycle per sec. are compared with the d.c. resistance at approximately 30 seconds after application of the e.m.f. Agreement is fair.