A certain copper wire has a resistance of 10.0 ?. At what

Chapter 16, Problem 16P

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QUESTION:

Problem 16P

A certain copper wire has a resistance of 10.0 Ω. At what point along its length must the wire be cut so that the resistance of one piece is 4.0 times the resistance of the other? What is the resistance of each piece?

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QUESTION:

Problem 16P

A certain copper wire has a resistance of 10.0 Ω. At what point along its length must the wire be cut so that the resistance of one piece is 4.0 times the resistance of the other? What is the resistance of each piece?

ANSWER:

Step 1 of 3

Let us assume that the length of the copper wire is  and its area is .

So the resistance is,

                                           

Here  is the resistance of the copper wire and  is the resistivity of the copper wire.

Now As copper wire is cit into two pieces of  and  such that

                                                           

                                                          

As,

                                                            

Substitute  for  in the above equation,

                                                               

And

                                                               

Therefore copper wire must be cut at  of the length.

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