Savchenko Problem 8.3.10
Physics · electromagnetism
Problem
In the Wheatstone bridge, the resistances are selected in such a way that the sensitive galvanometer connected to points A and B shows zero. Considering the resistances R , R , and r as known, determine the resistance r . If you 1 2 x swap the battery and the galvanometer, you will again get a bridge circuit. Is the balance saved in the new scheme?Intuitive explanation
A Wheatstone bridge achieves balance when the voltage drops across opposite arms are equal, making the galvanometer read zero—this happens when . The key insight is that balance depends on the ratio of resistances along each path, not on which component supplies power or measures the imbalance. Swapping the battery and galvanometer simply exchanges their roles, but the same resistance ratios still determine whether current flows through the galvanometer, so yes, balance is preserved.
Intuitive explanation
A Wheatstone bridge achieves balance when the voltage drops across opposite arms are equal, making the galvanometer read zero—this happens when . The key insight is that balance depends on the ratio of resistances along each path, not on which component supplies power or measures the imbalance. Swapping the battery and galvanometer simply exchanges their roles, but the same resistance ratios still determine whether current flows through the galvanometer, so yes, balance is preserved.