Two pieces of metallic wire having equal lengths and equal volume placed in air have different resistances. The two wires must

The resistance (R) of a metallic wire is determined by the formula R = ρ(L/A), where ρ is the resistivity, L is the length, and A is the cross-sectional area [c2][t5]. The volume (V) of a uniform wire is given by V = A × L. Since the problem states both wires have equal lengths (L) and equal volumes (V), their cross-sectional areas (A = V/L) must also be identical. Consequently, the geometric factors (L and A) are the same for both wires. According to Ohm's law and resistivity principles, if the dimensions are identical but the resistances differ, the difference must arise from the intrinsic property of the material, known as resistivity (ρ) [c2][t3]. Resistivity depends on the nature of the material and temperature [c2][t9]. Therefore, for two wires of identical dimensions to have different resistances in the same environment, they must be made of different materials.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.3 > p. 178