A cell of electromotive force (e.m.f.) 0.48 V is connected to a metal wire X, as shown in [Figure 6.1]. The cell has internal resistance. The current in the cell is 0.80 A. Wire X has length 3.0 m, cross-sectional area 1.3 × 10⁻⁷ m² and resistance 0.40 Ω.

1. (a)Calculate the charge passing through the cell in a time of 7.5 minutes. charge = ............................................................ C[2]
2. (b)Calculate the percentage efficiency with which the cell supplies power to wire X. efficiency = ............................................................ %[3]
3. (c)(i)There are 3.2 × 10²² free (conduction) electrons contained in the volume of wire X. For wire X, calculate: (i) the number density n of the free electrons n = ............................................................ m⁻³[1]
4. (c)(ii)(ii) the average drift speed of the free electrons. average drift speed = ............................................................ m s⁻¹[2]
5. (d)A wire Y has the same cross-sectional area as wire X and is made of the same metal. Wire Y is longer than wire X. Wire X in the circuit is now replaced by wire Y. Assume that wire Y has the same temperature as wire X. State and explain whether the average drift speed of the free electrons in wire Y is greater than, the same as, or less than that in wire X.[3]

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