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What happens to the wire in a fuse if it's current rating is exceed?

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it melts

The image above is one type of electrical fuse. This fuse has a specially designed wire inside glass housing. The wire inside the glass is made of a particular metal and with a particular thickness to give the wire an exact resistance. This resistance will allow passage of normal current plus a marginal percentage more. If, however, the current exceeds the allowed value, the wire in the fuse will heat and melt, thus interrupting current flow through the circuit. The fuse wire is placed in the glass housing and a fuse mount to insulate the melting wire from its surroundings. Any unintended increase in current, such as short circuits, overloading, mismatched loads, or device failure will cause the fuse to burn out  protecting the other parts of the circuit from overheating and further damage.

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