Question

A wire has a resistance of 27.2 ohms. It is melted down, and from the same volume of metal a new wire is made that is 3 times longer than the original wire. What is the resistance of the new wire?

Answer 1

Answer:

81.6 ohm

Explanation:

For a cable type conductor, the resistance is given by the following formula:

$R=\rho \frac{l}{S}$

Where:

$\rho=Material\hspace{3}resistivity\\l=Cable\hspace{3}length\\S=Cable\hspace{3}cross\hspace{3}section$

The problem doesn't give us additional information about resistivity or the cross section of the wire, so let's assume:

$S=constant\\\rho=constant$

Then, in this case, the resistance of the cable depends only on the length. Therefore, if its resistance was originally 27.2 ohms, if we triple its length, it makes sense that its new resistance is three times the original. Thus:

$R=3*(27.2)=81.6ohm$