Aluminum wiring has sometimes been used instead of copper...

Aluminum wiring has sometimes been used instead of copper for economy. According to the National Electrical Code, the maximum allowable current for 12 -gauge copper wire with rubber insulation is $20 \mathrm{A}$. What should be the maximum allowable current in a 12 -gauge aluminum wire if the power per unit length delivered to the resistance in the aluminum wire is the same as that delivered in the copper wire?

Key Concepts

Electrical Resistivity

Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. Different conductive materials, like copper and aluminum, have different resistivities, which means that for conductors of the same dimensions, the material with higher resistivity will have higher resistance. This concept is crucial for understanding why a conductor made of aluminum would need to operate at a lower current than one made of copper to produce the same heat (power per unit length) due to resistive losses.

Joule (Resistive) Heating

Joule heating, or resistive heating, refers to the process by which the passage of electric current through a conductor produces heat. The power dissipated as heat is given by the expression P = I²R, where I is the current and R is the resistance. Maintaining equal power dissipation in wires made of different materials requires adjusting the current based on the relative resistances of the materials.

Current Carrying Capacity

The current carrying capacity of a conductor is determined by its ability to handle heat generated by resistance to electric flow without damage or risk of fire. This capacity takes into account the material's properties, insulation type, and other factors like ambient temperature. In scenarios where the conductor material is changed, the allowed current must be recalculated to ensure that heat generation remains within safe limits.

Conductor Sizing and Wire Gauge

Wire gauge refers to the standardized sizes of conductors, where a specific gauge number corresponds to a certain cross-sectional area and inherent resistance per unit length. When comparing wires of the same gauge but made from different materials, such as copper versus aluminum, the difference in material properties such as resistivity becomes the determining factor for adjustments in their current ratings.

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