Determining the Resistance of a Wire
How can we calculate the resistance of a wire based on its properties?
Given a 20m length wire with a diameter of 1.5mm and a resistance of 2.5 ohm's, what is the resistance of a 3.5m length of the same wire with a diameter of 3mm?
Calculating the Resistance of the Wire
The resistive property of a wire is determined by its resistivity, length, and cross-sectional area. By comparing these properties for two wires of the same material, we can determine their relative resistances.
When calculating the resistance of a wire, we use the formula R = ρl/A, where R is the resistance, ρ is the resistivity of the material, l is the length of the wire, and A is the cross-sectional area of the wire.
In this case, for the wire with a 20m length and 1.5mm diameter, the resistance is given as 2.5 ohm's. To find the resistance of the wire with a 3.5m length and 3mm diameter, we need to consider the differences in length and diameter.
As the resistivity (ρ) of the material remains the same for both wires, the key factors affecting resistance are the length and cross-sectional area. Despite changing lengths and diameters, we can determine the resistance of the second wire using the concept of cross-sectional area.
Applying the formula:Resistance of the second wire (R) = ρ * length (3.5m) / cross-sectional area (A2)
By calculating the cross-sectional area for the second wire with a 3mm diameter and comparing it to the first wire, we find that the resistance of the 3.5m wire is 1.75 ohm.
Understanding how the properties of a wire affect its resistance can enhance our knowledge of electrical conductivity and applications in various fields.