Resistance vs Current: I ∝ m/a^2

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Discussion Overview

The discussion revolves around the relationship between current (I), resistance (R), and other physical quantities, particularly in the context of electrical circuits. Participants explore the implications of a proportionality statement involving current and mass/acceleration, questioning the appropriateness of the terms used and the underlying physics.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants suggest that resistance (R) should replace current (I) in the expression I ∝ m/a^2, indicating a potential misunderstanding or miscommunication regarding the terms used.
  • There is a suggestion that the expression lacks context, particularly regarding its application to electrical questions.
  • One participant emphasizes the importance of maintaining constant voltage when discussing the relationship between current and resistance, asserting that they are inversely proportional under that condition.
  • Another participant raises concerns about the interchangeability of symbols for resistivity (ρ) and density (d), questioning the logic behind their use in the provided attachment.
  • A later reply warns against drawing conclusions from algebraic manipulations without considering the physical implications, suggesting that mathematical relationships can sometimes lack meaningfulness in a physical context.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of the original expression and the symbols used, indicating that multiple competing interpretations exist. The discussion remains unresolved regarding the correct relationship and the implications of the terms involved.

Contextual Notes

There are limitations in the clarity of the original expression and its context, as well as potential misunderstandings regarding the symbols used for resistivity and density. The discussion highlights the need for careful consideration of physical implications when manipulating mathematical expressions.

gracy
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Should not there be R (resistance) instead of I (current)in the last line i.e
I ∝ m/a^2
 
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gracy said:
View attachment 82545
Should not there be R (resistance) instead of I (current)in the last line i.e
I ∝ m/a^2
If this is an electrical question, there's something missing from that final line...
 
XZ923 said:
If this is an electrical question,
Yes,It is.
 
XZ923 said:
there's something missing from that final line...
What's that?
 
gracy said:
What's that?
The answer is actually very similar to the one I posted in your previous thread...

I'm trying not to just give it away. Here's a hint: review Ohm's Law
 
It is a "proportional to" sign in the last line. It is a weird way to express the proportionality, however.
 
mfb said:
It is a "proportional to" sign in the last line. It is a weird way to express the proportionality, however.

Very true; I'm just not a fan of expressing a current-to-resistance proportionality without a requirement that "voltage remains constant".

To better answer the OP's question:
Assuming voltage remains constant, resistance and current are inversely proportional to each other
Assuming the physical makeup of the conductor remains the same, cross-sectional area an resistance are inversely proportional to each other
Therefore, assuming voltage and physical makeup of the conductor remain the same, current and cross-sectional area of the conductor are directly proportional
 
There's something I am not getting about the OP. The symbol ρ is commonly used for Resistivity and also for Density. It strikes me that the two appear to be used interchangeably in the attachment. I don't see the logic of the argument being used in that attachment. Can someone explain. please?
 
  • #10
Maybe she can provide more context. Is that from the internet?
Without context looks like a bizarre relationship.

They seem to use d for density and ρ for resistivity.
 
  • #11
@gracy
It is often possible to take two unrelated expressions, then re-arrange them, algebraically, assume that some of the variables in each expression are the same value and get an unexpected apparent relationship between two variables. It can be mathematically correct but of no meaningfulness in terms of the Physics at work. One needs always to be aware of the physical implications of such bits of maths manipulation.
 

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