Need help for wire thickness for power caps

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Well, how much will the peak discharge current be? Or continous? Then we can tell you better. (Or you can google "AWG current capacity" and get an idea what size wire would be good. You don't want the wire to melt, or its insulation to melt, or to introduce more resistance than what you had in mind to the circuit).
 
Is there a difference between copper wire and silver color wire?
copper wire can come plain, or insulated, or plated.

The plain copper oxidises quickly and the ends need to be cleaned to allow soldering. Old stranded copper wire cords/cables gradually go black as the oxygen permeates through the insulation. These are very difficult to clean and very difficult to solder reliably.

Insulated can be an enamel coating (thin paint like substance) or an insulating tube. Again the insulation needs to be removed to allow soldering.

Plated comes in three common forms: Tin plated (Sn), Tinned (Sn+Pb), Silver (Ag) plated. All these protect the copper from corroding and all can be soldered without further cleaning.
 
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