Problem 2.4   Source:   Problem 21 , page 161, HALLIDAY & RESNICK & WALKER, Jearl - Book: Fundamentos de Física - Vol 3 - Ed. LTC - 8ª ed.- 2009.

A wire with a resistance of 6.0 ohms is stretched in such a way that its length is makes it three times the size of the original. Determine wire resistance after operation assuming the resistivity and density of the material remain unchanged.

Solution of the Problem 2.4

As the problem says that the resistivity and the density of the wire remain unchanged during stretching means that there is no loss of material. In this way the volume of the wire remains constant. Then the new resistance of the wire will depend on its new length and its new area. The equation of the wire volume is given by:

Then, after stretching we will have a new area, A₂, and a new length (3 L). However, the volume is the same. So:

So the relationship between the areas is:

Remembering once again the equation that relates the resistance and its variables, we have:

Now, putting in this equation the new length (3 L) and the new area (A/3), we will find the resistance of the new wire.

Therefore we conclude that the value of the wire's resistance after stretching is nine times greater than its original value, or: