A cylindrical copper wire P of length 0.24 m is shown in [Figure 6.1]. The current in the wire is 0.85A. The resistance of the wire is 3.3 mΩ. The total number of charge carriers N in the wire is 2.6 × 10²². The resistivity of copper is 1.8 × 10⁻⁸Ωm.

1. (a)Calculate the potential difference between the two ends of the wire. potential difference = ................................................................V [2][2]
2. (b)(i)Show that the cross-sectional area of the wire is 1.3 × 10⁻⁶m².[2]
3. (b)(ii)Show that the number density of charge carriers in the wire is 8.3 × 10²⁸ m⁻³.[1]
4. (b)(iii)Calculate the average drift speed of the charge carriers (electrons) in the wire. average drift speed = ................................................................ms⁻¹ [2][2]
5. (c)A different copper wire Q has the same volume as wire P, but non-uniform radius, as shown in [Figure 6.2]. The radius r₁ at end X of wire Q is the same as the radius of wire P. Radius r₂ is less than r₁.
6. (c)(i)State and explain how the resistance of wire Q compares with the resistance of wire P.[4]
7. (c)(ii)On [Figure 6.3], sketch a graph of the variation of the average drift speed of the charge carriers with distance from end X of wire Q.[2]

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