Concept:Heat produced in a wire depends on its resistance, and resistance increases when the wire is thinner.
Explanation:When current
I flows through the wire, the heat generated per second is given by
P=I2R.
For a wire of resistivity
ρ and length
L, the resistance is
R=ρAL, where
A is the cross-sectional area.
A smaller diameter means a smaller cross-sectional area
A.
So, for the same material and length, the resistance becomes larger.
This larger resistance causes more heat to be produced in the wire, making it very hot.
Answer:The wire becomes very hot because it has a smaller diameter.