Calculating the Resistivity of a Conductor Wire: A Step-by-Step Guide

Understanding the resistivity of a conductor wire is crucial for various applications in electrical engineering and daily electronics. In this article, we will walk through the process of calculating the resistivity using the given dimensions and formula.

Understanding Resistivity

Resistivity (ρ) is an intrinsic property of a material that indicates how strongly the material resists the flow of electric current. It plays a significant role in determining the electrical behavior of materials. The resistivity is given by the formula:

Rho RA/L

Where:

R is the resistance of the conductor, A is the cross-sectional area of the conductor, and L is the length of the conductor.

Problem Statement

The length of a conductor wire is 10 meters. The diameter of the wire is 0.4 millimeters, and the resistance is 2 ohms. We are tasked with finding the resistivity (ρ) of the conductor wire.

Solving the Problem

To solve this problem, we need to follow these steps:

Calculate the cross-sectional area (A) of the conductor wire. Use the resistivity formula to find the value of ρ.

Step 1: Calculate the Cross-Sectional Area

The cross-sectional area of a cylinder is given by:

A πd^2/4

Where d is the diameter of the conductor wire.

Given: d 0.4 millimeters 0.0004 meters (to convert millimeters to meters) A π(0.0004)^2 / 4 A 3.14 × (0.0004 × 0.0004) / 4 A 3.14 × 0.00000016 / 4 A 0.0000001256 m2

Step 2: Calculate the Resistivity

Now that we have the area (A), we can use the resistivity formula:

Rho RA/L

Where:

R 2 ohms, A 0.0000001256 m2, and L 10 meters.

Rho 2 × 0.0000001256 / 10

Calculating the numerator:

Numerator 2 × 0.0000001256 0.0000002512

Dividing by the length:

Rho 0.0000002512 / 10 0.00000002512 Ω-m

The resistivity (ρ) of the conductor wire is 0.00000002512 ohm-meters (Ω-m).

Conclusion

Understanding the resistivity of a conductor wire involves knowing the relationship between resistance, length, and cross-sectional area. By following the steps outlined in this guide, you can calculate the resistivity of a conductor wire accurately.

For further information or to solve complex problems involving electrical conductivity, refer to additional resources on electrical engineering principles and materials science.