State the characterisitics of fuse wire.

Explanation

Consider a fuse wire of length l, area of cross section A and radius r.
Let I= current passing through the fuse wire
R= Resistance of the fuse wire.
Heat produced by current per unit time `=I^(2)R`
`=(I^(2) rho l)/(A) = (I^(2). Rhol l)/(pi r^(2))`...(i)
Let H is the heat loss per unit area of the wire.
Heat loss per see by curved part of the wire `= H.2pi rl`
As heat produced = Heat loss,
From (i) and (ii)
`(I^(2). rho l)/(pi r^(2)) = H.2pi rl`
`(I^(2) rho)/(2pi^(2) r^(3)) -H`
`I^(2)= (H(2pi^(2)))/(rho) r^(3)`
Thus, the current at which fuse wire melts is independent of the length of the wire.