For a proper functioning Wheatstone bridge, what must happen when measuring resistance in one of its branches?

In a Wheatstone bridge, the primary condition for proper functioning and accurate resistance measurement is that the bridge must be balanced. When a Wheatstone bridge is balanced, the ratio of the resistances in one pair of opposite branches is equal to the ratio of the resistances in the other pair. This balance results in no current flowing through the galvanometer, indicating that the potential difference between the two midpoints is zero.

For accurate resistance measurement, ensuring balance is crucial because any imbalance can lead to incorrect readings. The balance condition allows the user to calculate the unknown resistance with precision based on the known resistances in the other branches. This principle is fundamental to the operation of the Wheatstone bridge, making it an essential factor when conducting any measurements using this configuration.

While having constant current, stable temperature, or variable voltage may influence the measurements, they are not the main factors necessary for the function of the Wheatstone bridge itself. Balancing the bridge directly addresses the accuracy and reliability of the resistance measurement, making it the correct answer in this scenario.