the fuse is just another cable in the electrical circuit designed to melt when the current flowing through it crosses the current threshold in other words the fuse is the current protection device.
For example, a fuse wire 2a can carry current up to 2a without problems in both directions but once the current flows through the transverse axis 2a the wire melts and cuts other devices on the circuit to prevent damage.
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. so the fuse cord is made of enough thickness so that it allows desirable (2a if it is 2a fuse) current compared to other thick wires as it is designed to allow high currents (you can check the current ratings printed on your pc wire power supply). they are also designed to have low melting point.
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.if you want an intuitive explanation for the relationship between the thickness of the wire and the carrying capacity of this current, let me explain with a nice water pipe and water analogy.
As always wire = water pipe and water = current.
The conductor resistance is proportional to its length and inversely proportional to its cross-sectional area. so, if the fuse cable is thick, a larger cross section reduces the resistance across the fuse cable. so, even high currents flowing through the fuse, it does not explode. because it only serves as a normal electrical contact on a circuit or cable.
Resistance, r = p l / a
P – resistivity per unit length
L – length
A – area
To reduce the area and maintain the minimum resistance to generate heat, the fuse is made as thin.
Fuse wire should not have high resistance or low resistance. it must have sufficient power to carry its rated current without undesirable disconnection and immediately melt for a slight over current. it is the increasing fuse thickness with current rating.