Question

An electrician finds that a 1 m length of a certain type of wire has a resistance of 0.24 Ω . What is the total resistance of the 138 m of this wire he plans to use? Answer in units of Ω.

Answer 1

The resistance of a given conductor depends on its electrical resistivity ($\rho$), its length(L) and its cross-sectional area (A), as follows:

$R=\frac{\rho L}{A}$

In this case, we have $L'=138L$, $\rho'=\rho$ and $A'=A$. So, the total resistance of the wire with length of 138m is:

$R'=\frac{\rho' L'}{A'}\\R'=\frac{\rho 138L}{A}\\R'=138\frac{\rho L}{A}\\R'=138R\\R'=138(0.24\Omega)\\R'=33.12\Omega$