EPFO EO/AO 2023 General Ability Test · Question 87 of 120

Correct — A, (a) be doubled. Two relationships are combined here, and the item is testing whether the candidate can chain them without confusing which quantity is held fixed. The first is the resistance of a conductor. For a wire of uniform cross-section, resistance equals resistivity multiplied by length and divided by area of cross-section. Resistivity is a property of the material and does not change when a wire is cut; the area of cross-section is unchanged if the same wire is shortened rather than drawn out. So resistance is directly proportional to length, and halving the length halves the resistance. The second is Ohm's law. Current equals potential difference divided by resistance. The stem fixes the potential difference — 'for a given potential difference' is doing real work in that sentence — so the current is inversely proportional to the resistance. Resistance has been halved, therefore the current is doubled. That is option (a). Put end to end: current is proportional to potential difference divided by resistance, and resistance is proportional to length, so at a fixed potential difference the current is inversely proportional to the length. Halve the length, double the current. The same chain answers the neighbouring questions in this family — double the length and the current falls to a half; double the diameter and the area of cross-section is multiplied by four, so the resistance falls to a quarter and the current is multiplied by four. Two conditions are worth stating aloud because they are what makes the clean answer true. The wire must be shortened, not stretched: stretching a wire to a new length keeps its volume constant, so the cross-section shrinks as the length grows and the resistance rises as the square of the length ratio rather than in simple proportion. And the temperature must be treated as unchanged, since a metal's resistivity rises with temperature and a wire carrying twice the current will in fact run hotter. The paper's model assumes both, and under that model the current is exactly doubled.

• (b)be halved — This is the answer produced by applying the length relationship and then forgetting to invert it — the candidate correctly sees that resistance is halved and then halves the current as well, as though current followed resistance rather than opposing it. Ohm's law puts resistance in the denominator, so at a fixed potential difference the current moves the opposite way to the resistance. A halved current would require the resistance to be doubled, which would mean doubling the length, not halving it.
• (c)remain unchanged — This treats the current as a property of the wire or of the source rather than as the result of the two together. It would be right only if the resistance were independent of length, which contradicts the relation that resistance equals resistivity times length divided by area. The option also has a superficial appeal from a different quarter: in a series circuit the same current flows at every point, so a candidate may reason that the current 'does not change along the wire'. That is a statement about position within one circuit; the question asks about two different circuits, one with a wire of half the length of the other.
• (d)become zero — Nothing in the situation opens the circuit, and a shorter conductor conducts more readily rather than less. Current would fall to zero only if the path were broken or the potential difference removed, and the stem supplies a potential difference explicitly. The option is present as an obviously extreme choice, of the kind included to complete a set of four rather than to be seriously considered.

Resistance is not a fixed number attached to a substance; it depends on both the material and the shape of the piece. The relation that captures this is that resistance equals resistivity multiplied by length and divided by area of cross-section. Resistivity is the material property, measured in ohm metres, and it is what tables compare when they say copper conducts better than iron; length and area are geometry. Resistance therefore rises in proportion to length and falls in proportion to the area of cross-section, which is why a long thin wire resists more than a short thick one of the same metal. Ohm's law then converts resistance into circuit behaviour: at a constant temperature the current through a conductor is directly proportional to the potential difference across it and inversely proportional to its resistance. The two relations are chained constantly in practice. A house is wired with thick conductors on high-current circuits so that the resistance, and with it the heat and the voltage drop, stay small. A rheostat works by changing the length of resistance wire in the circuit. A fuse is deliberately made of a short thin piece of low-melting alloy so that it is the hottest point in the circuit and fails first. And resistivity itself rises with temperature in a metal, which is the qualification behind almost every idealised problem of this kind.

The science block of this paper draws on school physics and asks for a chain of two familiar relations rather than a calculation. The habit rewarded is reading the clause that fixes a quantity — here 'for a given potential difference' — because it tells the candidate which of the three variables in Ohm's law is the constant, and therefore which way the answer moves. Items in this family are usually answerable by proportional reasoning alone, with no numbers substituted at all.

• Resistance equals resistivity multiplied by length and divided by area of cross-section.
• For a given material and cross-section, resistance is directly proportional to length; halving the length halves the resistance.
• By Ohm's law the current at a fixed potential difference is inversely proportional to the resistance.
• Chaining the two, at a fixed potential difference the current is inversely proportional to the length of the wire.
• Doubling the diameter multiplies the area of cross-section by four, so the resistance falls to a quarter.
• Resistivity is a property of the material, measured in ohm metres, and does not change when a wire is cut.
• If a wire is stretched rather than cut, its volume stays constant, so resistance rises as the square of the length ratio.
• The resistivity of a metal rises with temperature, so idealised results assume the temperature is unchanged.

• Halving the current along with the resistance, forgetting that resistance sits in the denominator of Ohm's law.
• Confusing a wire that is cut shorter with a wire that is stretched longer; only the first leaves the cross-section unchanged.
• Reading 'the same current flows throughout a series circuit' as an answer to a question comparing two different wires.
• Overlooking the clause that fixes the potential difference, and reasoning as though the current were the fixed quantity.

Current-electricity items in EO/AO papers ask what happens to resistance, current or power when one variable is changed — length, thickness, material, voltage — and expect proportional reasoning rather than substitution. Learn the resistance formula and Ohm's law as a single chain, and rehearse the four standard changes: longer, shorter, thicker, thinner.

No directly related past PYQ was found.

• practice — not a real PYQ

  If the diameter of a wire is doubled, its length remaining the same, its resistance becomes :

  • (a)Four times
  • (b)Twice
  • (c)One-half
  • (d)One-fourth

  Answer(d) One-fourth

• practice — not a real PYQ

  The resistivity of a conductor depends on :

  • (a)Its length
  • (b)Its area of cross-section
  • (c)The material and the temperature
  • (d)The potential difference applied across it

  Answer(c) The material and the temperature