Resistance, wire thickness, fuses, current -- Confusion

[Barclay]

Homework Statement

In a book discussing a simple electrical circuit it said "If a thick wire is used in the experiment, the current will be extremely high for a very low voltage. The wire can get very hot very quickly".

This got me thinking about fuses in plugs. Is the fuse in a plug a thick wire so that it becomes hot a blows readily? I always thought it was a thin wire.

The statement made by the book is correct because:

resistance of wire ∝ 1/cross-sectional area

So as the wire thickens it's resistance decreases (so it is a low resistance wire).

V = IR

R ∝ 1/ I So because the resistance of this thick piece of wire is low it will take in high current and get hot.Or was I correct earlier when I thought that fuse wires are normally thin compared to the rest of the circuit so that they do not get hot and blow too readily?

Homework Equations

The Attempt at a Solution

 

[berkeman]

The wire in fuses is sized to blow for a given current and duration. Higher amperage fuses will be thicker than lower amperage fuses.

 

[lightgrav]

A wire gets hot (hot enough to burn skin, or melt its insulation off) because its Thermal Energy must flow thru its surface Area (to outside).
Thick wire carries a similar current density (I/A) as thin wire , for a given local E-field (V/m).
fuse wire is typically thinner than "household wire" so that it gets hot enough to melt itself, carrying only a few Amps.