Fuse: why does it connect in parrallel with resistor?
This fuse holder has a small neon bulb in series with the resistor.  The neon bulb acts as an indicator that the fuse has blown.

When the fuse is intact, the voltage across the fuse is small.  So is the voltage across the neon light with resistor, because it's in parallel with the fuse.  When the fuse blows it becomes open circuit, and the supply voltage appears across the neon bulb with resistor.  The neon bulb lights up.  The purpose of the resistor is to limit the current through the neon bulb.


  Wired across the fuse terminals and contained in the plastic cover is a resistor and neon indicator that would presumably light up if the fuse was ruptured.  [from Amazon product customer review]