CDS (I) 2020 General Knowledge · Question 25 of 120

Correct — C, ohm-cm. Resistivity comes from the relation between resistance, length and cross-sectional area: R equals rho times length divided by area, so rho equals R times area divided by length. Substituting units gives ohm times square centimetre divided by centimetre, which is ohm-centimetre. In SI the same argument gives the ohm-metre, and that is how the quantity is formally defined — a cube of material one metre on a side with a resistance of one ohm between opposite faces has a resistivity of one ohm-metre. Ohm-centimetre is the same quantity in centimetre-gram-second units, and it is still common in materials data.

• (a)ohm — The ohm alone is resistance, which depends on the shape and size of the specimen. Resistivity is the material property left after the geometry is divided out.
• (b)ohm/cm — Ohm per centimetre puts the length in the wrong place. The formula multiplies resistance by an area and divides by a length, which leaves one length in the numerator.
• (d)ohm-cm² — Ohm times area, with no division by length. This is the units of resistance times area, and it does not reduce to resistivity.

Resistance measures how strongly a particular object opposes current and depends on the material, the length and the thickness of that object. Resistivity measures how strongly the material itself opposes current, independent of shape. Two copper wires of different lengths and diameters have different resistances but the same resistivity. The SI unit is the ohm-metre; conductivity is the reciprocal and is measured in siemens per metre.

Every option is built from ohms and centimetres, so once again the unit has to be derived rather than recalled. Start from R equal to rho L over A, make rho the subject, and put units in. It is also worth carrying a sense of scale, because resistivity spans an enormous range and questions often ask for a ranking rather than a unit: silver about 1.6 × 10⁻⁸ ohm-metre, nichrome about 110 × 10⁻⁸, and glass anywhere from 10¹¹ to 10¹⁵ ohm-metre. Nichrome is used for heating elements precisely because its resistivity is some seventy times silver's while it remains a conductor.

• Resistance R equals resistivity times length divided by cross-sectional area.
• The SI unit of electrical resistivity is the ohm-metre; ohm-centimetre is the CGS equivalent.
• Resistivity is a property of the material alone; resistance also depends on the object's dimensions.
• Silver has a resistivity of about 1.6 × 10⁻⁸ ohm-metre, nichrome about 110 × 10⁻⁸, and glass 10¹¹ to 10¹⁵.
• Electrical conductivity is the reciprocal of resistivity and is measured in siemens per metre.

• Answering ohm, which is resistance and not resistivity.
• Inverting the length, giving ohm per centimetre.
• Assuming a longer or thinner wire of the same metal has a higher resistivity; only its resistance changes.

As the unit of resistivity, or as a which-wire-has-the-highest-resistivity item designed to test that resistivity is shape-independent.

• practice — not a real PYQ

  Three copper wires of different lengths and different thicknesses are taken. Which one of the following is the same for all three?

  • (a)Resistance
  • (b)Resistivity
  • (c)Current for a given voltage
  • (d)Cross-sectional area

  Answer(b) Resistivity — it is a property of the material, so it is identical for all three, while their resistances differ.

• practice — not a real PYQ

  The SI unit of electrical resistivity is

  • (a)ohm
  • (b)ohm per metre
  • (c)ohm metre
  • (d)siemens per metre

  Answer(c) ohm metre — siemens per metre is the unit of the reciprocal quantity, conductivity.