Physics Electronics PMDC Conceptual Practice
PMDC Verified Question 328 of 494
What is the general expression for the electrical conductivity \( \sigma \) of an extrinsic semiconductor with electron density \( n \), hole density \( p \), and mobilities \( \mu_n \) and \( \mu_p \)?
A
σ = q × (n + p)
B
σ = q × (n μn + p μp)
C
σ = (n μn) / (p μp)
D
σ = q / (n μn + p μp)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: σ = q × (n μn + p μp)
Concept:

Total electrical conductivity \( \sigma \) is the sum of the drift current contributions from mobile electrons in the conduction band and mobile holes in the valence band.

Formula:

$$\sigma = J / E = q n \mu_n + q p \mu_p = q (n \mu_n + p \mu_p)$$

Solution:

  • Electron contribution to conductivity: \( \sigma_n = q n \mu_n \).


  • Hole contribution to conductivity: \( \sigma_p = q p \mu_p \).


  • Summing both carrier types gives \( \sigma = q (n \mu_n + p \mu_p) \).


Why other options are incorrect:

  • Option A: Omits carrier mobilities \( \mu_n \) and \( \mu_p \).
  • Option C: Conductivity is the sum of contributions, not a ratio.
  • Option D: \( 1 / [q(n\mu_n + p\mu_p)] \) defines electrical resistivity \( \rho \), the reciprocal of conductivity.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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