How do the (i) thickness and (ii) length of a fuse wire depend on its current rating?
(i) Thin fuse wires are used to increase the resistance. If the current is high, the fuse wire has to melt and for that, a wire as thin as possible is needed.
(ii) The length and current rating of fuse wire are independent. Fuse wire can conduct current to any lengths, but thickness which controls the melting is important.