A fuse is a deliberately weak link in a circuit: a short piece of wire chosen so that when current exceeds a set value, the heat it generates (proportional to I²) melts the wire and breaks the circuit. Its protective action depends entirely on its rated current being matched to the circuit it guards.

If the fuse rating is set higher than the circuit's safe (maximum) current:

• A fault can push current well above what the wiring and components can safely handle, yet still stay below the fuse's melting threshold.
• The fuse therefore never gets hot enough to blow, so it fails to disconnect the supply — the components can overheat or be damaged while the fuse sits intact.

This is exactly the symptom described — an overcurrent fault occurs but the fuse does not blow — so an over-rated fuse is the most likely cause and the correct answer.

The other options do not explain the failure. Correct practice is actually to connect a fuse in series with the load so that all the load current passes through it; a fuse in parallel would carry no load current and is simply a wiring error, not the usual reason a properly placed fuse fails to trip. A fuse wire naturally has low resistance — that is by design so it does not waste power in normal use — and low resistance alone does not stop it from melting on overcurrent. Whether the fuse sits before or after a protective relay does not change the fact that fault current still flows through it; positioning relative to the relay is a coordination detail, not the reason it stays intact during a genuine overcurrent.