# 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?

Let

After melting and recast let

Now from (1)

And for initial wire

Dividing (4) by (3) we get

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Or

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

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The resistance of the new wire will be five times the original resistance (5R).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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