What diameter must a copper wire have if its resistance is to be the same as that of an equal le

step 1 We are given an aluminum wire, an aluminum wire of diameter 3 .26 millimeter. We want to find ou

What diameter must a copper wire have if its resistance is...

Key Concepts

Resistivity

Resistivity is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. It is denoted by the symbol ? and is essential in determining how much resistance a conductor will have per unit length and cross-sectional area regardless of its size.

Resistance of a Conductor

The resistance of a conductor can be calculated using the formula R = ?L/A, where R is resistance, ? is the resistivity of the material, L is the length of the conductor, and A is its cross?sectional area. This relationship highlights how both the material properties and the geometric factors of the conductor influence its overall resistance.

Cross-sectional Area

The cross-sectional area of a cylindrical conductor, such as a wire, is given by A = ?(d/2)^2, which shows that the area is proportional to the square of its diameter. Understanding this concept is key when comparing wires of different diameters, especially when maintaining equal resistance across materials with different resistivities.

Material Comparison

When comparing conductors made of different materials, the distinct resistivities of the materials become the determining factor. To achieve the same electrical resistance in wires of equal length, adjustments in the dimensions (such as the diameter) must be made to account for the differences in resistivity. This concept underpins the method of matching resistance between wires made from different metals.

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