The correct answer is C) sparking at the brushes. A shorted armature coil in a DC motor can be detected by the presence of sparking at the brushes. When an armature coil becomes shorted, it creates a localized weak spot in the magnetic field, leading to uneven current distribution and increased resistance. This causes the affected armature coil to draw more current, resulting in sparking at the brushes as they pass over the shorted coil. The other options are incorrect because: A) undercut mica is a maintenance procedure for commutator maintenance, not for detecting shorted armature coils; B) a shiny armature coil is not a reliable indicator of a shorted coil; and D) worn grooves in the armature are more likely to be caused by other issues, such as mechanical wear, and do not specifically indicate a shorted armature coil.