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A certain copper wire has a resistance of 10.0 ?. At what
Chapter 16, Problem 16P(choose chapter or problem)
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?
Questions & Answers
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.