State, qualitatively, the relationship of the resistance of a metallic wire to its length and to its cross-sectional area

Resistance of a Metallic Wire

Key Concepts

Resistance (\$R\$) is a property of a material that opposes the flow of electric current. For a uniform metallic wire the resistance depends on three main factors:

• Material (its resistivity, \$\\rho\$)
• Length of the wire (\$L\$)
• Cross‑sectional area of the wire (\$A\$)

Qualitative Relationships

The following statements describe how the resistance changes when the length or the cross‑sectional area of a metallic wire is varied, keeping the material and temperature constant.

1. Increasing the length of the wire increases its resistance.
2. Decreasing the length of the wire decreases its resistance.
3. Increasing the cross‑sectional area of the wire decreases its resistance.
4. Decreasing the cross‑sectional area of the wire increases its resistance.

Quantitative Relationship (for reference)

The quantitative form of the relationship is given by the resistivity equation:

\$R = \\rho \\frac{L}{A}\$

where \$\\rho\$ is the resistivity of the material (a constant for a given metal at a given temperature).

Summary Table

Suggested Diagram

Example Question

Question: A copper wire of length \$2.0\,\$m has a resistance of \$0.5\,\\Omega\$. If the length is doubled while the cross‑sectional area remains the same, what will be the new resistance?

Answer (qualitative): Doubling the length doubles the resistance, so the new resistance will be \$1.0\,\\Omega\$.