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For a resistor of uniform cross-section carrying current, if the current is doubled while temperature remains approximately constant, which of the following statements are correct?

1. The current density is doubled
2. The conduction electron density is doubled
3. The mean time between collisions remains constant
4. The electron drift speed is doubled

Correct answer: The current density is doubled

Solution

When current doubles in the same wire (area constant): (1) J = I/A doubles — correct. (2) Conduction electron density n depends on the material and temperature, not on current — unchanged, so this is INCORRECT. (3) Mean collision time tau = m/(ne² rho) depends on temperature and material properties, not on current; at constant temperature it is constant — correct. (4) Drift speed v_d = I/(neA) = J/(ne); since J doubles and n is constant, v_d doubles — correct. So statements (1), (3), (4) are correct and (2) is wrong.

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