The characteristics of a fuse are primarily determined by the internal construction.
You could think of a fuse as the weakest link in an electrical circuit. This weak point in the circuit is designed to fail before the rest of the circuit. An excessive current causes the fuse to heat up and then melt. This is typically accompanied by an electrical arc sustained by the inductive nature of many circuits and by the plasma containing molecules of the melting fuse link.
To understand the operation of a fast fuse we need to explore the dynamics of the melting wire. Consider the normal fuse show in in the upper left panel. It is a simple length of wire. Excessive current causes the wire to melt starting. The current will continue to flow via the arc until the gap in the melting wire is large enough to extinguish the arc. This arc is like a blowtorch.
Contrast this with the fast fuse shown on the right side. A typical fuse element is segmented with alternating thin and thick pieces. In this sketch, the bridge elements are thin. These thin bridge elements are the weak points.
Excessive current will overheat the bridges. We can then expect many of the bridges to melt is rapid succession. Consequently, many small arcs form where the bridges once were. The arc is like a bunch of candles.
With all of that said, we come to the heart of your questions. It is easier and faster to naturally extinguish the small arcs than it is to extinguish the large arc.
Best Wishes,
APDahlen
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