Practice question

**Mobility** μ = v_d/E = e τ/m, τ relaxation time (s), measures ease of electron drift under field E (V/m). Conductivity σ = n e μ = 1/ρ, linking microscopic τ to macroscopic resistivity, explaining why metals conduct well due to large n and τ. Stretching doubles length ( l' = 2l ) and halves area ( A' = A/2 ) due to volume conservation. Resistance becomes R' = rho (2l) / (A/2) = 4R . Current I' = V / (4R) = I/4 . Current density j = I / A , so j' = I' / A' = (I/4) / (A/2) = I