The accurate determination of capacitance

THE PRINCIPAL OBJECTIVE of the work described in this paper is as follows: to develop a new method for accurately determining the capacitance associated with two-dimensional composite regions. The term capacitance refers to the ordinary electric capacitance associated with two charged conductors. However, the method is also directly applicable to the determination of the permeance of magnetic fields, the shape factor of thermal fields and to other analogous situations. “Accurately determine” is taken to mean determination of the capacitance with errors in the order of one part in one thousand. Although such accuracy has been claimed for certain electrolytic tank analog methods, it is usually possible only after careful attention is given to each source of error. Such errors can arise in both the construction and the measurements associated with the analog solution. In the present method, electrically conducting paper models, much easier to construct, are used and only ordinary care is required in the measurement techniques. The usual errors encountered in the use of such paper models, amounting to several per cent, are avoided by utilizing analytical methods to obtain a first approximation amounting to perhaps 90% of the final result, and using the paper analogs to determine the other 10%. Thus, the error in the final result will be in the order of a few per cents, of say 10%, or in the order of a few tenths of 1%.