Calculation of unknown components in "unbalanced" bridge circuit
When a bridge is balanced, you know that there is no voltage between Va and Vb, and as a consequence, there is no current flowing between them as well. This vastly simplifies the circuit analysis, making it easy to determine the unknown component(s) relative to the known ones.

For small values of imbalance, it is possible to linearize the analysis around the balance point, which retains some of the simplicity, but for large values of imbalance, you're forced to do the full analysis of the entire circuit. It can be done, but you've given up all the advantage of using a bridge in the first place. Other circuit topologies would actually be simpler to analyze.