Question

What is the resistance (in Ω) of a 17.5 m long piece of 17 gauge copper wire having a 1.150 mm diameter?

Answer 1

In order to calculate the resistance of this wire, we can use the formula below:

`R=(\rho d)/(A)`

Where p is the resistivity, d is the length and A is the cross-sectional area of the wire.

The resistivity of the copper is 1.72 * 10^-8 ohms*m, so we have:

`\begin{gathered} R=(1.72\cdot10^(-8)\cdot17.5)/((\pi\cdot(1.15\cdot10^(-3))^2)/(4))\\ \\ R=(30.1\cdot10^(-8)\cdot4)/(\pi\cdot1.3225\cdot10^(-6))\\ \\ R=(120.4\cdot10^(-8))/(4.1547563\cdot10^(-6))\\ \\ R=28.98\cdot10^(-2)\text{ ohms}\\ \\ R=0.2898\text{ ohms} \end{gathered}`