NDA (II) 2016 General Ability Test · Question 131 of 150

Correct — C, the claim that resistivity depends on the length and the area of cross-section of the wire. It does not. Resistance does — resistance equals resistivity multiplied by length and divided by area — but resistivity is the property of the material itself, the resistance that a unit cube of that substance would offer. Draw a copper wire out to twice its length and its resistance changes; its resistivity does not budge. Resistivity depends on what the wire is made of and on its temperature, and on nothing about its shape. That is precisely why the two quantities are given separate names and separate units, the ohm and the ohm metre.

• (a)The SI unit of charge is ampere-second — This statement is correct, so it cannot be the answer to a 'not correct' stem. Current is defined as charge per unit time, so charge equals current multiplied by time, and one coulomb is exactly one ampere-second.
• (b)Debye is the unit of dipole moment — Also correct. The debye is the customary non-SI unit for electric dipole moment, used constantly in chemistry to report molecular polarity; water is about 1.85 D. The SI unit is the coulomb metre, and one debye is roughly 3.336 x 10⁻³⁰ coulomb metre.
• (d)The kinetic energy of an electron of mass m kg and charge e coulomb, when accelerated through a potential difference of V volt, is eV joule — Correct as well, and the mention of the mass m is a deliberate red herring. Work done by the field equals charge multiplied by potential difference, and starting from rest all of it appears as kinetic energy, so the energy is eV joule regardless of the mass. The mass decides the final speed, not the energy.

Resistance and resistivity are related but different. Resistance is a property of a particular object and is measured in ohms; resistivity is a property of the substance and is measured in ohm metres. For a uniform wire of length l and cross-sectional area a, resistance R equals resistivity multiplied by l and divided by a. Because that formula already carries the geometry, the resistivity term standing outside it must be geometry-free. Resistivity does vary with temperature, and that is its only common dependence at school level — it rises with temperature for metals and falls for semiconductors.

A 'not correct' stem needs all four options read to the last word, and the paper-setter has loaded three of them with real physics that happens to be true. The quickest route is to spot the one statement that mixes up an object property with a material property. If you are unsure, test option (c) with a thought experiment: stretch a wire to twice its length while halving its area, and its resistance goes up fourfold — but nobody would say the copper has become a different material, and resistivity is a claim about the material.

• Resistance R equals resistivity multiplied by length and divided by area of cross-section; resistivity itself is independent of both length and area.
• The SI unit of resistance is the ohm and of resistivity the ohm metre.
• One coulomb equals one ampere-second, since charge equals current multiplied by time.
• The debye is the customary unit of electric dipole moment, about 3.336 x 10⁻³⁰ coulomb metre; the dipole moment of a water molecule is roughly 1.85 D.
• An electron starting from rest and accelerated through a potential difference V gains kinetic energy eV, which is what defines the electron volt.

• Treating resistivity as if it behaved like resistance; only resistance carries the geometry.
• Bringing the mass into the energy calculation for an accelerated electron — the mass fixes the speed, not the energy gained.
• Reading a 'not correct' stem as 'correct' and marking the first true statement you meet.

NDA leans hard on the resistance-against-resistivity distinction, sometimes as a direct definition item and sometimes buried inside a multi-statement question like this one, so make the material-property point automatic.

• practice — not a real PYQ

  A uniform wire is stretched so that its length becomes twice the original while its volume stays the same. Its resistivity then

  • (a)becomes twice
  • (b)becomes four times
  • (c)becomes half
  • (d)remains unchanged

  Answer(d) remains unchanged — the resistance becomes four times, but resistivity is a property of the material and does not depend on the shape.

• practice — not a real PYQ

  An electron and a proton are each accelerated from rest through the same potential difference. The kinetic energies they gain are

  • (a)equal in magnitude
  • (b)in the ratio of their masses
  • (c)in the inverse ratio of their masses
  • (d)in the ratio of their radii

  Answer(a) equal in magnitude — the energy gained is charge multiplied by potential difference, and the two carry equal magnitudes of charge; only their final speeds differ.