A copper wire is 2.0 mm thick and 2 meters long. What is the resistance?

To calculate the resistance of a copper wire, we can use the resistivity formula:

• R is resistance (unit: ohms, Ω)

• ρ is the resistivity of the material (unit: ohms · meters, Ω·m)

• L is the length of the wire (unit: m, m)

• A is the cross-sectional area of the wire (unit: square meters, m²)

For copper wires, the resistivity is approximately 1.72×10−8Ω⋅m (the standard value at 20°C).

First, we need to calculate the cross-sectional area A of the wire. Suppose the wire has a circular cross-section and a diameter of 2.0 mm, so the radius r is 1.0 mm, or 0.001 m. The formula for the area of A circle is A=πr 2, so:

Therefore, a copper wire with a diameter of 2.0 mm and a length of 2 meters has a resistance of about 0.01094 ohms under standard conditions (20°C). Note that the actual resistance value may vary slightly depending on the quality of the copper, temperature, and other factors.