# 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