Question

A wire of 5 ohms resistance is drawn so that it's new length is two times the original length. If the resistivity of the wire remains the same and the cross sectional area is halved, the new resistance is?

Answer 1

The resistance can be found as follows:

$$R=\rho\dfrac{L}{A},$$

here, $\rho$ is the resistivity of the wire, $L$ is the length of the wire and $A$ is the cross sectional area of the wire.

Since $L_{new}=2L$, $\rho_{new}=\rho$ and $A_{new}=0.5A$, we get:

$$R_{new}=\rho_{new}\dfrac{L_{new}}{A_{new}}=\rho\dfrac{2L}{0.5A}=4\rho\dfrac{L}{A}=4R,$$ $$R_{new}=4\cdot5\ \Omega=20\ \Omega.$$