In our jumping ring apparatus the coil creating the magnetic field is plugged into a wall socket, so it is receiving alternating current at an effective average voltage of 120 V.
Would the apparatus give the same results if we connected it to a 120-volt battery instead?
No. There is a current continually induced in the ring because the magnetic field set up by the coil is constantly changing. If we tried to use a DC system (like a battery) when we first closed the switch we would change the flux through the ring, momentarily inducing an emf, but then the flux would be constant so there would be no induced current in the ring.