The reason for galvanometers to be not used in AC bridges:
In an AC bridge, a galvanometer is not used because the rotating torque is dependent on the average current that is passing through the coils of a galvanometer.
But the average current passing through the AC bridge will be zero.
The magnetic field depends upon the direction of the electric current.
In AC the direction of the current keeps reversing at a constant period so the magnetic field also reverses its direction.
So, there will be no deflection in the galvanometer.
So there will be no current passing through the coils of the galvanometer which leads to zero rotating torque in galvanometer which leads to zero deflection of the needle in the galvanometer.
Therefore, a galvanometer is not used in an AC bridge.
Hence, the galvanometer is not used in AC bridges.