Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A wire has a resistance of . It is stretched evenly until it is times its first length. Its volume does not change. What is its new resistance?
: the resistance grows with the length, falls with the area, and depends on the material through its resistivity (in ). Change square millimetres to square metres: .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The length. times as long: rises times.
Step 2. The area. The volume is fixed, so the area falls to : rises times again.
Step 3. Together. .
Answer: .
Common mistake. forgets that the wire also gets thinner.
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