# [Physics] Resistance of aluminium rectangular wire

electrical-resistanceelectromagnetism

I am working on upgrading an electromagnet design program. There are currently two types of wire used for the coil, circular and strip (read as: rectangular).

The current algorithms in this program are empirically derived with lots of undocumented constants and so one of the requirements is to move it more into the realm of accepted physics.

The formula I am using to calculate resistance is:

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

These are aluminum wires so the value of $\rho$ boils down to $2.82\times10^{-8}$ at 20°C.

For circular wires this works perfectly, giving near enough the same results (enough to put it down to the increased accuracy).

For strip wires this doesn't work quite so well. The problem comes from a difference in the cross-sectional area of the wire.

The original program is doing $h^2$ as the area, where $h$ is the height of the wire. Now is that not wrong? The cross-sectional area should be $wh$ where $w$ is the width of the wire.

For example,
If the strip wire is 8.4mm by 2.8mm, the original program would do:

$$2.8 ^ 2 = 7.84$$

but should it not be doing:

$$8.4\times2.8 = 23.52$$

The entire original algorithm is:
$$R = \frac{84.09L}{h^2}$$

Is there a reason the original engineer may have done $h^2$ as apposed to the correct cross-sectional area?

I don't want to just declare his calculations as wrong as the results from this program have been used for the last 30 years and none of the magnets have gone bust or underperformed. Infact if anything they would have been over performing if this calculation is wrong.