Resistivity

A long wire has more resistance than a short one. A thick wire has less resistance than a thin one. So R = ρl/A, where l is the length, A the area of cross-section and ρ (rho) the resistivity. The SI unit of resistivity is the ohm metre, Ω m.

Cut a copper wire in half and its resistance halves. Its resistivity does not change, because it is still copper. Metals and alloys have very low resistivity. Alloys have higher resistivity than pure metals and do not burn easily, so heater coils use them. Resistivity also changes with temperature.

A small example

A wire 2 m long has an area of cross-section of 1 × 10⁻⁶ m². Its resistance is 0.2 Ω.

• ρ = RA/l.
• ρ = (0.2 Ω × 1 × 10⁻⁶ m²) / 2 m.
• ρ = 1 × 10⁻⁷ Ω m.

Where marks go

Question 34 of CBSE's 2026-27 Science sample paper has a resistivity option, set as an internal choice. The 2026-27 Science marking scheme gives 1 mark for the definition with R = ρL/A. It gives 1 more for showing, with an example, that resistivity depends "only on material (not on dimensions)".

In a numerical, put the area in m² and the length in m, so that ρ comes out in Ω m. If a wire's size is given in centimetres, change it first. Changing units is part of the working.

About the author

Deepti Sardana

Founder Member & Academic Lead

An IIT alumna (M.Sc., M.Phil.) with over 25 years in teaching, child psychology and learning assessment. As Academic Lead at EduBrahma, she leads the method TRUtesting uses to find where and why a child loses marks.

Deepti Sardana on LinkedIn