The resistivity ρ of a material may be expressed in units of
- A.ohm
- B.ohm/cm
- C.ohm-cm
- D.ohm-cm²
Correct answer
Explanation
The correct answer is C, ohm-cm. Resistivity equals resistance multiplied by area and divided by length, which leaves the unit ohm × length.
From R = ρl/A, resistivity ρ = RA/l. Area has the unit cm² and length cm, so ρ has the unit ohm × cm²/cm = ohm-cm; in SI it is the ohm-metre (Ω m). Resistivity is a property of the material itself: copper and silver have very low resistivity, while nichrome, used in heater coils, has a high value. It changes with temperature but not with the size or shape of the wire.
A is wrong because the ohm is the unit of resistance, which depends on the wire's length and area.
B is wrong because ohm per cm would be resistance per unit length, not resistivity.
D is wrong because ohm-cm² has one length unit too many; it would be resistance times area without dividing by length.
Exam tip: resistance in ohm (Ω), resistivity in ohm-metre (Ω m); conductivity is its reciprocal, siemens per metre.
Practice Questions
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- B.Martin Luther
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- D.Copernicus
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