Answer: If the bridge is balanced, the galvanometer reading will be the same with the key open or closed.
Explanation:
Unbalanced bridge: The potentials of points A and B are different. When the key is closed, current flows through the lead AB, and, therefore, the distribution of all the currents in the circuit changes. This is equivalent to a change in the entire resistance of the circuit and results in a change in the current flowing through the battery. In an unbalanced circuit, the galvanometer reading will change when the key is opened or closed.
Balanced bridge: The potentials of points A and B are the same. The current distribution in the circuit and the current flowing through the battery do not change, regardless of the position of the key.