What is the Correct Definition of Dynamic Resistance and Resistivity?

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Discussion Overview

The discussion centers on the definitions of dynamic resistance and dynamic resistivity, exploring their mathematical formulations and applications, particularly in the context of diodes and current density.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant defines dynamic resistance as Rd = dV/dI and questions if it can also be expressed as Rd = d(IR)/dI, leading to Rd = R + I dR/dI.
  • Another participant agrees with the definition of dynamic resistance as dV/dI, noting its relevance to diode junctions.
  • A different participant suggests a potential definition for dynamic resistivity as ρD = dE/dJ, linking it to electric field and current density.
  • One participant expresses confusion regarding the definition of dynamic resistivity and proposes a formulation ρd = d(Iρ)/dI = ρ + I dρ/dI.
  • A participant shares an external article related to the topic, though its relevance is not discussed further.

Areas of Agreement / Disagreement

Participants generally agree on the definition of dynamic resistance as dV/dI, but there is no consensus on the definition of dynamic resistivity, with multiple formulations proposed and some confusion expressed.

Contextual Notes

There are unresolved assumptions regarding the definitions and applications of dynamic resistance and resistivity, particularly in how they relate to different contexts such as diode behavior and current density.

tiny-tim
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I'm confused about dynamic resistance.

The definition I've seen is Rd = dV/dI.

Is it also ok to write it Rd = d(IR)/dI, so that Rd = R + I dR/dI ?

I couldn't find a straightforward definition for dynamic resistivity at all …

is it ρd = d(Iρ)dI = ρ + I dρ/dI ?
 
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Dynamic resistance is dV / dI. It is often used to refer to the dynamic forward resistance of a diode junction, or the dynamic resistance of a zener diode junction.
 
If RD = dV/dI, then a reasonable definition for dynamic resistivity would be
ρD = dE/dJ,​

where E is electric field and J is the current density.
 

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