Is there any ultra strong electrical wire at about AWG24 (0.22mm)? I want something that would be strong as a steel wire rope but also with low resistance that can used as electrical wire.
Electronic – Strongest electrical wire at AWG 24
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If you remove the cap you'll have a metal dingus where you can solder a wire to. You then have a test lead which can hook onto wires, IC pins, resistor leads, you name it. Use it to make signal or power connections or as measuring leads to a DMM.
They allow for finer work than alligator clips, which serve the same function:
It's a good idea to have some test leads within reach, and to have them in different colors, so that you can tell the signals apart easily when the wiring becomes spaghetti-like; for instance use black for ground and red for your positive power supply.
You are likely to get some good ideas here - all images connect to a related webpage.
Something like these adapters would allow you to connect two threaded studs together which should meet your need.
This arrangement is similar - tube with both ends threaded.
Something like this can have the cable from above entering from the opposite end to the stud (black as shown here, but with an end that is wider than the exit hole so it cannot escape. The stud is screwed in from the other and and tightens against the broad end of the cable.
Items like these and like these are not suitable directly but may give ideas.
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Best Answer
Since you are using 5V ("5V and the current 0.5A" from a comment), you probably have two limitations, one based on heating and one based on voltage drop. The second may well be the long pole in the tent.
Incidentally, your 0.22 mm diameter number is wrong for AWG24 wire diameter (it's actually a bit over 0.5mm diameter), so it's not clear to me whether you are keying off the gauge or the diameter.
In any case, you might be able to kill two birds with one stone by using a switchmode regulator along with a relatively high voltage such as 24VDC.
Assuming, say, 85% efficiency, 2.5W at the destination will require about 3W input or 125mA at 24VDC. The loop resistance of 0.255 mm (AWG 30) steel wire 1m long (x2 for return path) would be around 8 ohms, so it would drop about 1V, costing about 5% in efficiency. Not too bad. One watt spread over 2m of wire is not too much either.