IIT JEE , AIEEE Forum - Physics , Electricity

KAB

Sir,

How to derive,

i²

r³

where,

i is the maximum current that can pass through the fuse wire without melting.

r is the radius of the fuse wire.

Is it applicable to any wire or only fuse wire?

bhupesh

Dear
The derivation could be as follows
Heat

Mass ( Mass = density times volume )
Heat

Density Volume
For a wire you can treat it as cylinder with volume
2

r h ( h =length of the cylinder )

Heat = i²R t ( R

h/a R = Resistance )
a =

r²
we can write

i²

density (Volume ) (

r² /h) { Cross multiplying }
Volume=2

rh , Substituting this

i²

r³

As far as fuse is concerned the wire has to be of high melting point for any wire this will not be practically apllicable

KAB

Sir if we treat fuse wire as a cylinder then shouldn't its volume be

r^2h?and doesnt fuse wire has low melting point?

sabya_sachi

the answer does not clearly prove i^2

r ^3

bhupesh

Dear

First I am sorry for the mistake while deriving over the computer I had mistaken

You are right

Actually

H=i² Rt
H/t=i² R

H/t = rate of heat loss And rate and heat loss takes place mainly due to radiation
from stefans law = H/t=

A T⁴A= Surface area which is 2

rh

Now you can replace R =

L/A ( A = Cross sectional area

r²⁾

sorry for the in convenience and T⁴ will be treated as constant for given temperature

KAB

Thank you sir.

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