Heating produced in a wire has to do with it's resistance times square of the current. For a given resistance, heating increases with the square of the current. However, Ohm's law relates voltage to be the product of the current and the resistance. Therefore, the rate of heating (i.e., power) has to do with the product of current and voltage. Thus [email protected]
will produce exactly the same heating in any given wire as [email protected]
Your 30A fuse wire will have the same gauge as our 15A fuse.
Not sure what that was all about, but:
The bottom line is that wire and breaker size is all about getting the most power to a load with the least voltage drop for the least cost.
A 120 volt 20 amp #12 wire circuit is the most common circuit across the country. 120 volt 15 amp #14 wire circuits are mostly for lighting. (One reason for not installing the 15 amp circuits for receptacles if that someone is sure to come along and plug in a heater, toaster, whatever).
Anyway, the desired result is to deliver power to the load with (usually) no more than a 3% voltage drop. Thus a 20 amp #12 circuit is the minimum desirable for a workshop, or for that matter, residential outlets. This will handle most domestic appliances, and in the shop most hand power tools as well as the smaller table saws, jointers, planers, etc, up to about a 2HP or so limit.
Now, if the run is long, (and this applies to any 120 or 240 volt circuit) at some point the voltage drop will exceed 3%, and the solution is to either increase wire size, or increase the voltage. If a 120 volt load can be switched to 240, then that's one solution, which requires only a different breaker. However this can only be done if it is not a circuit with a number of outlets.
If, however, the circuit in question is already a 240 Volt circuit, an increase in wire size is the only practical solution. An example here would be a 3HP compressor being replaced by a 5 HP model.
Bear in mind also, as the current requirements increase a number of different connection requirements come into play.