Evaluation of the NBS unit of resistance based on a computable capacitor

Abstract

An e valuat ion of t he uni t of resistance ma in tain ed at t he Natio na l Burea u of Stan da rds, based on t he prototype stand a rds of le ngt h and t ime, is d escribed. The evalu at ion is based o n a no min ally one-picofa ra d ca p a~i tor whose valu e m ay be calc ul a ted fro m its mec ha nical dimen. lio ns to hig h acc uracy. This capac ito r is used to calibrate a n O.Ol-micl"Ofar ad capacito r. A fr equency-dep enden t bridge in volving t his ca pac itor e~tab li s h es t he value of a lO'-ohm resisto r. Co mpa rison of t hat re.;istor wi t h t he ba nk of o ne-o hm res isto rs maintaining t he NBS uni t of resista nce es ta blis hes t hat t his unit is flB U= l.000002 3 ohms ± 2.1 ppm.Th e in d ica ted un certa in ty is an est imated 50 percent error of t he repo rted value based on t he s tat io t ica l uJl certain ty o f t he meas urements a nd a ll owin g for kn own so urces of p ossible sys te mat ic errors ot her t han in t he sp eed of li g ht , a ss uming t ha t t he speed o f li g ht c = 2.997925 X J QIO c m/sec.

Improved 1-kHz capacitance calibration uncertainty

“…At NIST, the calculable capacitor and associated measurements, which form the basis for the capacitance unit, were developed at a frequency of 1592 Hz [1,2]. This frequency was chosen because the calculable capacitor was also the basis for the resistance unit and at that frequency a conve nient connection between the capacitance and resistance can be made.…”

Standard cells :

“…The ohm in absolute measure may also be obtained using a computable capacitor [18]. In this method the evaluation of resistance is based on a nominally 1-pf capacitor whose value in es units may be calculated with high accuracy from its dimensions and thence in em units using the speed of Ught.…”

“…A conventional d-c step-down is then used to provide "absolute" calibration of d-c resistors of lower magnitude, specifically 1 ohm. For more details, reference [18] should be consulted. The overall precision (repeatability) of the method is about ±2 ppm.…”

“…Cutkosky [18] The emf of any or all standard cells could be determined in like fashion. Obviously, such a procedure would be cumbersome and time consuming and if required would be unfortunate, indeed.…”

“…Absolute measurements are involved, require painstaking work and, therefore, are unsuitable for frequent or routine measurements of emf. To circumvent the necessity for frequent absolute measurements, standard cells^are constructed, their emfs are determined in relation to current and resistance in absolute measure, and these cells are then used to maintain the volt; these This value differs by 1.7 ppm from ihat (I.OOOOO23) published by Cutliosky [18).…”