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IB · B · multiple choice

The particulate nature of matter · Question 4

The particulate nature of matter · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
routine
Marks
1
Topics
1
Answer
Complete
Two wires of the same material, drawn to compare their dimensionswire 1: length L, diameter d, resistance RLdwire 2: same material, length 2L, diameter 2d2L2d
Figure 1Two wires of the same material are drawn one above the other, each as a long bar seen from the side. The upper one is labelled wire 1: length L, diameter d, resistance R, with a dimension line under it marking L and a small dimension at its end marking the diameter d. The lower one is drawn twice as long and twice as thick and labelled wire 2: same material, with dimension lines marking 2L along it and 2d across its end.
multiple choice1 mark

A wire of resistivity ρ, length L and cross-sectional area A has resistance R. A second wire of the same material has twice the length and twice the diameter. What is its resistance?

  1. A

    R/2

  2. B

    R

  3. C

    2R

  4. D

    4R

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Answer overviewCorrect answer: A — R/2
01

Answer and reasoning

1 mark
How to approach it

Predict from the governing principle before looking for a matching option. Then reject alternatives by checking direction, units, limiting behaviour or the physical meaning of each statement.

  1. 1

    The correct choice is A: R/2

  2. 2

    C doubles for the length and forgets that the area depends on the square of the diameter. Doubling the diameter quadruples the area, so the two changes give 2/4 = ½.

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