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27.10. The current in a wire is doubled. What happens to (a) the current density (b) the conduction-electron density (c) mean time between collisions, and (d) the electron drift speed? Are each of these doubled, halved, or unchanged?

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Final answer:

When the current in a wire is doubled, the current density and electron drift speed double, while the conduction-electron density and mean time between collisions remain unchanged.

Step-by-step explanation:

When the current in a wire is doubled:

(a) The current density doubles because it is directly proportional to the current assuming the cross-sectional area of the wire remains constant.

(b) The conduction-electron density remains unchanged as it depends on the material properties and not the current.

(c) The mean time between collisions remains unchanged since it is a characteristic of the material and the temperature, which are assumed to be constant.

(d) The electron drift speed doubles, given that drift velocity is proportional to current for a given conductor with constant charge carrier density and cross-sectional area.

For the Practice Problems: Doubling the voltage across an ohmic resistor also doubles the current through the resistor, according to Ohm's law.

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