Resistance bridge sensitivity and output formulas

CONVENIENT FORMULAS for current and voltage in the detector branch of a resistance bridge are shown in Figures 1 to 3. These formulas are particularly useful for determining either the exact sensitivity of the balanced bridge or the approximate output of the unbalanced bridge where the unbalance is, in general, not greater than the order of 10 per cent. In either case, the user is assumed to be referring to and working from the balanced-bridge condition. The proportional error of the output approximation, based on the exact output value, does not exceed the proportional unbalance of the bridge (for example, no more than a 1-per-cent error results if the bridge is out of balance by 1 per cent). It does not matter whether the values of V, I, C, T, S, and D are taken from the balanced or from the unbalanced bridge, although it is more convenient to take them from the former. The formulas in Figure 3 are of course not new, being merely representations of Thevenin's Theorem, but they nonetheless belong in this group to complete the logical assembly of formulas.