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Electrical wiring connections or splices must be made inside junction boxes, so choose one near or accessible to the cabinet to use as your power source. Shut off the circuit breaker for the wire you intend to splice to. Install a 14-gauge or 12-gauge Romex cable in the junction box, but do not connect the wires at this point.
Run the Romex cable to the base cabinet below where you plan to install the light. If the wiring is in a basement with an unfinished ceiling, drill a 3/8” hole through the floor and the bottom of the base cabinet, and use fish tape to pull the cable up into the cabinet. If you don't have access to an unfinished basement, run the wiring to the cabinet from another junction nearby.
From inside the base cabinet, drill a hole at an upward angle through the cabinet back into the wall cavity behind it.
Above the wall cabinet where you plan to install the light, drill a 3/8" hole into the wall cavity. Push the fish tape through the hole into the cavity and down to the bottom hole. Hook the tape to the Romex and pull it up through the cavity, then out through the top hole.
Install a metal junction box on top of the cabinet, near the back wall and out of sight from below. Run the Romex into the box and use a cable clamp to secure it in place.
Connect a receptacle outlet to the Romex cable, attaching the black wire to the outlet’s brass screw, and the white wire to its silver screw. Attach the bare Romex ground wire to the outlet’s green screw. Install the outlet in the junction box and attach a cover.
Place the transformer on top of the cabinet, near the junction box, and plug its power cord into the outlet. The transformer reduces the home’s 120-volt electrical current to a safe level suitable for low-voltage fixtures such as halogen lighting. Transformers for this application typically have two brass screw connections for attaching the fixture wires.
Determine where you will mount the light fixture and how you will run the wiring to the transformer. Drill a 3/8” hole in an inconspicuous spot in the underside of the cabinet and in the top of the cabinet.
Use screws to mount the fixture, insert the bulb and attach the lens.
Feed the wires from the light fixture to the transformer and connect them.
If the light fixture does not have a switch, attach a self-connecting inline switch to the wiring where it is conveniently accessible. To install this switch, remove the back and lay one wire inside the switch, following the manufacturer's instructions. Replace the back and tighten it to complete the installation.
When all of the above steps are complete, return to your original power source and connect the Romex cable wiring to the wires in the junction box. Use wire nuts to secure your connections.
Switch on the power to the circuit and test the light fixture operation.