Which one of the following correctly represents the SI unit of resistivity?

Correct — D, ohm-metre (Ω m). Resistivity ρ is defined through R = ρL/A, so ρ = RA/L. Substituting units gives ohm × metre² ÷ metre = ohm-metre (Ω·m), which is the SI unit of resistivity.

Why the others are wrong

• (a)
  Ω — The ohm alone is the unit of resistance (R), not resistivity; resistivity carries an extra length factor beyond resistance.
• (b)
  Ω/m — Ohm per metre inverts the length dependence. Rearranging ρ = RA/L shows the metre multiplies rather than divides, giving Ω·m, not Ω/m.
• (c)
  Ω cm — Ohm-centimetre is a practical unit used in some industries, but it is not the SI unit; the SI unit is built on the metre, giving Ω·m.

The resistance R of a uniform conductor depends on both material and geometry: R = ρL/A, where L is length, A is cross-sectional area and ρ is resistivity. Resistivity is the intrinsic, material-specific property; rearranged, ρ = RA/L, which gives units of Ω·m.

Key facts

• Resistivity is defined by R = ρL/A, so ρ = RA/L.
• The SI unit of resistivity is the ohm-metre (Ω·m).
• Resistivity is a property of the material, independent of the wire's length or thickness.
• Good conductors such as copper have very low resistivity (about 1.7 × 10⁻⁸ Ω·m); insulators have very high resistivity.

Common traps

• Quoting the ohm (unit of resistance) instead of ohm-metre.
• Writing Ω/m by inverting the length factor in ρ = RA/L.

• practice — not a real PYQ

  The reciprocal of resistivity is called

  • (a)conductance
  • (b)conductivity
  • (c)resistance
  • (d)impedance
  Answer(b) conductivity — conductivity σ = 1/ρ, measured in siemens per metre (S/m).
• practice — not a real PYQ

  If a copper wire is stretched to twice its length at constant volume, its resistivity

  • (a)doubles
  • (b)halves
  • (c)remains the same
  • (d)becomes four times
  Answer(c) remains the same — resistivity is a material property; only the resistance changes with geometry.