How do a wire’s length and cross-sectional area affect its resistance?

The resistance of a wire is determined by its physical dimensions and the material from which it is made. These relationships are expressed by the formula $R=\rho \frac{l}{A}$, where $R$ is resistance, $\rho$ is the resistivity of the material, $l$ is the length, and $A$ is the cross-sectional area.12

The effects of length and area on resistance are as follows:

• Length ($l$): Resistance is directly proportional to the length of the wire. As the wire becomes longer, the resistance to the flow of charge increases because the current must travel a greater distance.23
• Cross-sectional Area ($A$): Resistance is inversely proportional to the cross-sectional area of the wire. A larger cross-sectional area provides more space for charge carriers to move, resulting in a smaller resistance to the flow of current.23

In summary, increasing the length of a wire increases its resistance, while increasing its cross-sectional area decreases its resistance.3