What is the connection provided on DC motors that supplies the armature with power via brushes?

The connection that supplies the armature with power in DC motors via brushes is indeed a commutator. The commutator is a mechanical switch that reverses the direction of current flow through the armature winding as the motor rotates. This is essential in ensuring that the torque produced by the motor remains in a consistent direction, allowing for continuous rotation.

As the brushes make contact with the commutator segments, they enable the flow of electrical current to the armature winding. This process allows the armature to interact with the magnetic field produced by the stator, ultimately generating torque that drives the motor. The design of the commutator facilitates efficient current switching, which is critical for the functionality of DC motors.

The other options, while related to electrical systems, do not fulfill the role of providing power to the armature in the context of DC motors. Field poles refer to the stationary magnets or windings that create the magnetic field necessary for the motor's operation, while slip rings are used primarily in alternating current (AC) applications to provide a continuous connection to rotating components. Lastly, a hard-wired connection does not allow for the necessary switching functionality required in a DC motor setup.