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I installed water proof LED 5630 strip lighting under my kitchen cabinets. I used a kit of sorts with a small transformer and a remote dimmer switch. Initially, it worked, but flickered at the end of the run. An electrician suggested I remove the remote dimmer, so I installed an in line on/off switch. That didn't help, so I purchased a different transformer at 12V/5A capacity. The lights are now real dim with the end of the run not lighting. The "run" is: 40" of single strand double wire from transformer to 41" light strip...170" of multi strand speaker wire going up in attic, over sink, then down and to a 20" light strip...then jumpered to 22" light strip...jumpered to another 22" light strip...jumpered to 57" light strip. I checked the transformer on a 5 meter length of strip lights and it worked fine. I'm not sure what my next step should be, and any help is appreciated.

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You're run is too long. Each LED strip will draw considerable current and add quite a bit of resistance to the run. You don't say what gauge wires you have in between, but here is a rough guide for how far you can run a 12V line:

           24 AWG    22 AWG    20 AWG    18 AWG      16 AWG      14 AWG      12 AWG
DC 100mA  216 feet  342 feet  594 feet  867 feet  1,379 feet  2,197 feet  3,508 feet
DC 200mA  108 feet  171 feet  297 feet  433 feet    689 feet  1,098 feet  1,755 feet
DC 300mA   72 feet  113 feet  198 feet  289 feet    459 feet    732 feet  1,169 feet
DC 400mA   54 feet   85 feet  148 feet  216 feet    344 feet    549 feet    877 feet
DC 500mA   43 feet   68 feet  119 feet  173 feet    275 feet    439 feet    701 feet
DC 750mA   28 feet   45 feet   79 feet  115 feet    183 feet    293 feet    467 feet
DC 1000mA  21 feet   34 feet   59 feet   86 feet    137 feet    219 feet    350 feet

Basically, speaker wire is relatively thin and LED strips draw considerable current. If it were me I would probably not daisy chain all the strips together. Try wiring them in more of a star topology where each new LED strip connects to a splice off from a single voltage bus (wire). Consider upgrading your power carrier to a 12 or 14 gauge wire.

The current draw will depend on the actual number of LEDs in each strip, but from the distance you've quoted you might be very close to or over the 5A of the transformer.

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    The strips themselves don't have a lot of "gauge" in them either, and on a long run, you will see voltage drop. You can break them up, or just feed them at multiple points. – DaveM Apr 6 '17 at 2:30

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