Which one of the following correctly represents the SI unit of resistivity?
- (a)Ω
- (b)Ω/m
- (c)Ω cm
- (d)Ω m
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.
- (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.
Students confidently pick Ω (the unit of resistance) or invert the length dependence to Ω/m. The clean route is to derive the unit straight from ρ = RA/L: (Ω)(m²)/(m) = Ω·m.
- 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.
- Quoting the ohm (unit of resistance) instead of ohm-metre.
- Writing Ω/m by inverting the length factor in ρ = RA/L.
Either a direct unit-recall ('SI unit of resistivity?') or a reasoning item on how resistivity differs from resistance.
No directly related past PYQ was found.
- 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.