If a wire of resistance #R# is melted and recast into a wire of length #2/5#th that of the original wire, what is the resistance of the new wire?
2 Answers
Let
After melting and recast let
The volume of the material of the wire in both state will be same. So
Again it is given that
Now from (1)
Let
Then for initial wire
And for initial wire
Dividing (4) by (3) we get
So the resistance of the new recast wire will be
Or
Explanation:
During the recasting process the same volume of metal that was melted was used to form the new wire. For that reason we know that the volume (
Volume is related to the length and cross-sectional area of the wire by the relationship:
I will define the initial dimensions of the wire as
Initial resistance of the wire is:
The question specifies that the length is reduced to
Also
Now that we have expresssions for both
Or