I did try the higher ranges first. I thought that was implied.I explained the likely reason in post #44, you had the meter set to much too small a range, so much too high a resistance.
As I showed (with pics!) in post #50; -- as it seems my earlier statement: " Good continuity between cable and foil both sides; and total isolation side to side. " was not enough for you -- there is nothing wrong with the connections.this assuming the 'soldered' connections to the foil are working (which is dubious) and that the foil itself is making good electrical contact.
Short the wires on my adapter together, and the phone powers up and is completely usable with the adapter in place.
Earlier you said:
No - aluminium doesn't solder (with normal tin/lead solder) - so you don't ever try to solder it. You can get special aluminium solder, but I've no idea if that would solder to copper or not?.
See How to Solder copper wire to aluminum foil.; and Soldering Aluminium with an Iron for the explanation for why the solder beads on aluminium despite successfully wetting. (Short version: It only wets where the oxide layer has been a) removed & b) been prevented from reforming by the exclusion of air.)
No, the charging circuit will almost certainly be crude, nasty, and really horrible - probably just a single resistor.
There seem to be an awful lot of heavyweight components for this to be a crude and nasty circuit:
And doesn't explain how a 4.5V minimum chip runs off 2.4v.
Eg. The component bottom right labelled WJ3 is likely a " SOT-23-5 Linear voltage regulator IC LDO, 3.5V±1%, 200mA, +CE, CL, PDR" which also requires at least 4.5V input to produce its 3.5v regulated output.
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