When fuses are connected in series it is difficult to discriminate the fuse unless the fuse has significant size difference. The larger diameter of the bigger wire offers more area for electrons to move through the circuit. For this reason, smaller gauge wire is rated for lower amperage electric current limits than larger gauge wire.
The smallest size of common household wire can carry 15 amps of current. Which material is generally used in a fuse wire? Answer: An alloy of lead and tin as it has a low melting point and a very high resistance.
This low resistance means that the voltage drop across the fuse will be very small. The thicker the wire the more current is needed to melt it and the higher the 'rating' of the fuse. The purpose of a fuse is to protect the wiring and the equipment. If the fuse was not there and something went wrong the wires themselves would get hot and maybe catch fire.
The fuse is generally connected in series with the device to be protected. So we do not want fuse wires with high resistance the relationship between wire thickness and current carrying capability is that, more thickness more current can be carried by wire. The fuse wire has no high resistance or low resistance, only has enough resistance and low melting point to produce enough heat to melt when excessive current flows through it.
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