Question

A 7.8-meter long copper wire has a diameter of 3.3x10exp(- ) 2 m. Determine the resistance of the wire.

Answer 1

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

$R=\frac{p\cdot L}{A}$

Where p is the resistivity, L is the length and A is the cross-section area.

For copper, we have p = 1.72 * 10^-8.

Then, using L = 7.8 m and A = pi*r² (area of a circle), we have:

$\begin{gathered} R=\frac{1.72\cdot10^{-8}\cdot7.8}{\pi\cdot(\frac{3.3}{2}\cdot10^{-2})^2} \\ R=\frac{13.416\cdot10^{-8}}{3.1416\cdot2.7225\cdot10^{-4}} \\ R=\frac{13.416\cdot10^{-8}}{8.553\cdot10^{-4}} \\ R=1.57\cdot10^{-4} \end{gathered}$

Therefore the wire resistance is 1.57 * 10^-4 ohms.