Usually the task of a Wheatstone or Thomson bridge is to find such conditions, under certain given conditions, so that the sensitivity of the circuit is greatest. Meanwhile, it is known that when measuring large and very small resistances, the sensitivity of the circuit decreases, and it may happen that even the highest possible sensitivity at such resistances will be lower than required. Therefore, it seems interesting to find out what the lowest and highest resistances can be measured with the required relative accuracy on the Wheatstone or Thomson bridge and what the corresponding resistances in the remaining branches should be under certain given conditions. This article solves the problem of determining the minimum and maximum resistances measurable on the bridge with a given accuracy for a given maximum current sensitivity of the galvanometer and its internal resistance under the following conditions (see article). In addition, the article shows that when measuring low resistances, both bridges - Thomson and Wheatstone - can be used with equal success.