The Variation with Frequency of the Power Loss in Dielectrics

Abstract

Variation of the power loss in dielectrics with frequency, 500 to 1,000,000 cycles.—(1) A new bridge method of measurement is described. This bridge has two resistance ratio arms, and two similar variable condenser arms which are made to act as pure capacities by connecting their dielectrics in parallel with the resistance arms. The condenser to be studied is connected in parallel with one of the bridge condensers set at zero. With this bridge the equivalent series resistance can be obtained directly without the assumption that the loss in the standard condenser is negligible. The theory of this bridge is given. For frequencies above 3,000 a resonance substitution method was used, correction being made for the losses in the standard precision condenser. (2) Results for glass, Pyrex, paraffin, ceresin, mica and Murdock composition are given. The power loss for unit voltage is equal to $2\pi \mathrm{fCF}$, where $f$ is the frequency, $C$ the capacity and $F$ the power factor, which depends only on the material. Since the phase difference is small, $F$ is taken equal to $2\pi \mathrm{fCR}$, where $R$ is the equivalent series resistance. It was found that, approximately, $R=\frac{A}{f^k}$, $P=B{f}^n$; hence $F=\frac{D}{f^{\mathrm{}(k-n)\mathrm{}}2}$. For paraffin, mica, and Pvrex, the values found for $D$ are.00174,.0132, and.0264; the values of ($k-n$) are.30,.23, and.215, respectively; and the values of ($n+k$) are all close to 2, the difference being due to the small change of capacity with frequency. (3) Relation to phenomenon of residual charge. The constant $n$ is the same as in the equation of E. v. Schweidler for the residual charge current: $i=E{C}_0\beta t^{-n}$, where $E$ is the harmonic impressed electromotive force and $\beta$ is a constant. This equation leads to the above equation for power loss and also to the equation for the capacity: $C=C_0(1+M{f}^{n-1\mathrm{}})$, where $M$ is a constant. Values of $n$ determined from the variation of capacity with frequency agree closely with those given above. This agreement both confirms the theory and indicates the accuracy of the measurements.