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CE A cylindrical wire is to be doubled in length, but it
Chapter 21, Problem 89GP(choose chapter or problem)
Problem 89GP
CE A cylindrical wire is to be doubled in length, but it is desired that its resistance remain the same,
(a) Must its radius be increased or decreased? Explain,
(b) By what factor must the radius be changed?
Questions & Answers
QUESTION:
Problem 89GP
CE A cylindrical wire is to be doubled in length, but it is desired that its resistance remain the same,
(a) Must its radius be increased or decreased? Explain,
(b) By what factor must the radius be changed?
ANSWER:
Solution 89GP
Step 1 of 2
Here we need to find whether the radius of the cylindrical wire should be increased or decreased when its length is doubled by keeping resistance constant.
- The resistance of the wire in the initial case is given by,
Where and are the length and area of the wire, is resistivity of wire.
- The resistance of the wire in the final case when the length is doubled is given by,
Where and are the length and area of the wire, is resistivity of wire.