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GATE 2025 PH – Question 17

Solid State Physics · conductivity, electron and hole statistics in intrinsic and extrinsic semiconductors, mobility and effective mass · 1 mark · Multiple choice

As per the Drude model of metals, the electrical resistance of a metallic wire of length $L$ and cross-section area $A$ is (consider $\tau$ as relaxation time, $m$ as electron mass, $n$ as carrier concentration and $e$ as electronic charge)

  1. $mL/(ne^2A\tau)$
  2. $2mL/(ne^2A\tau)$
  3. $mL/(2ne^2A\tau)$
  4. $mL/(4ne^2A\tau)$

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Correct answer: (A) $mL/(ne^2A\tau)$

Explanation

**Drude model.** Free electrons accelerate in the field $E$ and are scattered with a mean time $\tau$ between collisions. The current density is
$$J=\sigma E,\qquad\sigma=\frac{ne^2\tau}{m} .$$

**Resistance of a uniform wire** of length $L$ and cross-section $A$:
$$R=\frac{L}{\sigma A}=\frac{mL}{ne^2\tau A}\quad(\text{option A}).$$