A wire 1 mm in diameter is connected to one end of a wire of the same material 2 mm in diameter of twice the length. A voltage source is connected to the wires and a current is passed through the wires. If it takes time T for the average conduction electron to traverse the 1-mm wire, how long does it take for such an electron to traverse the 2-mm wire

T = 2 T₀

Explanation:

To answer this question let's write the expression for electrical conductivity

    σ = n e2 τ / m*

The relationship with resistivity is

       ρ = 1 /σ

Whereby the resistance

        R = ρ L / A = 1 /σ  L / A

We see that there is no explicit relationship between time and resistance, there is only a dependence on the life time (τ) that depends on the properties of the material, not on its diameter or length.

As also the average velocity or electron velocity of electrons is constant, the time to cross 2 mm in length is twice as long as the time to cross a mm in length

 T = 2 T₀