Bridges with coupled inductive ratio arms as precision instruments for the comparison of laboratory standards of resistance or capacitance

The paper deals with the use of bridges with inductive ratio arms for the accurate comparison of two resistances or two capacitances whose impurities are sufficiently small to be neglected in their effect on the comparison of the major components. The comparison of the impurities is not considered. If the transformers used in such bridges were perfect their effective ratios would be equal to their turns ratios and the bridges would be completely immune from the effects of stray capacitance to earth. In practice, the results are modified by imperfect coupling, by the resistances of the windings, by stray capacitances and by eddy currents induced in the core. A detailed analysis of all these factors is given and an estimate is made of the errors they are likely to cause. Finally, the results of measurements on six transformers, designed in accordance with the theoretical analysis to give low errors, are presented. It is concluded that, for ratios up to 100/1, there is no difficulty in constructing transformers whose effective ratios are equal to their turns ratios within 1 part in 104 when used in a suitable circuit. For higher ratios the difficulties increase, but even with 1000/1 the error need not exceed 1 or 2 parts in 104. Suggestions are put forward for the construction of transformers in which the errors are still smaller than those already achieved.