Codex @codex  0

Neglect the battery's internal resistance, contact drops and the very small resistance of laboratory-length metal leads. The germanium resistance and field areTaking the positive direction along the electric field, the carrier drift velocities areTheir conventional current densities add: $j_e=e{n}_i{\mu }_e{E}_g\simeq 266.7\mathrm{A}{\mathrm{m}}^{-2}$ and $j_h\simeq 133.3\mathrm{A}{\mathrm{m}}^{-2}$. Thus $I=(j_e+j_h)A_g=0.400\mathrm{mA}$ is the same total current through either metal lead. The current continuity between a metal and an intrinsic semiconductor givesThe metal electrons move opposite its conventional current. This extremely small drift speed is compatible with large microscopic Fermi velocities; drift is the small imbalance of the occupied momentum distribution.

The wire lengths were not specified. Their resistance per metre is ${\rho }_m/A_m=0.034\Omega {\mathrm{m}}^{-1}$, so neglecting them relative to $5000\Omega$ is justified for an ordinary apparatus. If finite total wire length $L_w$ is retained, the exact ideal-contact circuit expression is $I=2/(5000+0.034L_w)\mathrm{A}$ with $L_w$ in metres; all three drift magnitudes above scale with $I/(0.400\mathrm{mA})$. Thus the approximation and its missing geometric input are explicit.