What does the vertical line in this equation mean?

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Discussion Overview

The discussion centers around the interpretation of a vertical line in a mathematical equation, specifically in the context of electrical engineering and the behavior of bipolar transistors. Participants explore the meaning of this notation and its implications for understanding the equation's application.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants propose that the vertical line indicates the ratio is evaluated at a constant value of I_b.
  • Others suggest it means "evaluated at," indicating a specific point for calculating derivatives or approximations.
  • A participant mentions that the equation appears to relate to the dynamic emitter-collector resistance of a bipolar transistor, interpreting the ratio as the change in emitter-collector voltage over the change in collector current.
  • One participant expresses uncertainty about the exact meaning, noting that the equation might have a physical interpretation beyond the mathematical notation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the precise meaning of the vertical line, with multiple interpretations and some uncertainty remaining about its implications in the context of the equation.

Contextual Notes

There are unresolved assumptions regarding the definitions of terms used in the equation and the specific conditions under which the interpretations are valid.

APUGYael
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Hey,

What does the vertical line with the "I_b" on the bottom right mean?
Link here: https://imgur.com/a/nII9g

Thanks,

-Yael
 
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I believe it means the ratio is evaluated at a constant Ib
 
It usually means "evaluated at". It indicates the point where derivatives are calculated to actually turn into a linear approximation. As there is no derivative, I assume that either ##c## is approaching ##b## or at least ##b \in I_c## and ##I_c## is closing down on ##\{b\}##.

For the record, the image reads ##r_{ce} = \left.\dfrac{\Delta U_{ce}}{\Delta I_c}\right|_{I_b}## but maybe it means something else, as it looks like a physical equation.
 
@fresh_42 I believe the equation is the dynamic emitter collector resistance for a bipolar transistor. in this case the ratio of the change in emitter collector voltage over the change in the collector current.
 
gleem said:
@fresh_42 I believe the equation is the dynamic emitter collector resistance for a bipolar transistor. in this case the ratio of the change in emitter collector voltage over the change in the collector current.
I suspected something like this. Actually I had a déjà vu as I wrote the answer, which was why I added the physical possibility. Strange thing.
 

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