Making the sum of 2 resistors independent of 1 of them

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Discussion Overview

The discussion revolves around the question of whether it is possible to make the total current in a series circuit of two resistors independent of the value of one resistor by increasing the value of the other resistor. Participants explore the implications of resistor values on current flow in a circuit powered by a voltage source.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants propose that increasing the value of one resistor could make the total current independent of the other resistor's value, but this idea is met with skepticism.
  • One participant suggests using a double-potentiometer to maintain constant total resistance as one resistor changes, implying a complex solution to the problem.
  • Comparative analysis is presented, showing the current through a 1-Mega-Ohm resistor versus a series combination of a 1-Mega-Ohm and a 1-Milliohm resistor, highlighting the minuscule difference in current.
  • Another participant emphasizes that the current remains dependent on both resistances, questioning the feasibility of achieving independence through resistance manipulation.
  • A later reply humorously suggests making one resistor infinite as a potential solution, indicating a theoretical approach rather than a practical one.
  • Concerns are raised about the significance of small differences in current measurements, with references to the limitations of calculators versus analog methods.

Areas of Agreement / Disagreement

Participants do not reach a consensus. There are competing views on whether it is possible to achieve independence of current from one resistor by adjusting the other, with some arguing against the feasibility of such an approach.

Contextual Notes

Discussions include assumptions about the behavior of resistors in series and the implications of theoretical versus practical measurements. The conversation reflects uncertainty regarding the limits of current independence based on resistor values.

brainbaby
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I am really not sure about this ...
I may be generalizing it ...but anyway...

suppose we have two resistors in series...connected by ofcourse a voltage source...and a certain amount of total current is flowing through the whole circuit..

now if we want to make the total current totally independent of the value of one resistance then do we have to make the value of other resistor very high...?

independent here means...no matter what is the value of that resistance.. it does not effect the total current
 
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brainbaby said:
I am really not sure about this ...
I may be generalizing it ...but anyway...

suppose we have two resistors in series...connected by ofcourse a voltage source...and a certain amount of total current is flowing through the whole circuit..

now if we want to make the total current totally independent of the value of one resistance then do we have to make the value of other resistor very high...?

independent here means...no matter what is the value of that resistance.. it does not effect the total current
The current is entirely dependent on the sum of the two resistors so the only way to to what you are asking (assuming I understand what you are asking, which I'm not sure about since what you are asking really doesn't make sense) is to devise a double-potentiometer with a single control mechanism so that as one of the two resistances goes up, the other goes down by an equal amount so as to keep the total resistance the same.
 
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Compare the current through a 1-Mega-Ohm resitor with the current drawn by a series combination of 1 Megohm and 1 Milliohm.
 
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LvW said:
Compare the current through a 1-Mega-Ohm resitor with the current drawn by a series combination of 1 Megohm and 1 Milliohm.
with 1megaohm individual resistor ...current is 2*10^-5A...whereas with series combination it is 1.999999998*10^-5A...

but what is the conclusion in reference to the problem...?
 
brainbaby said:
with 1megaohm individual resistor ...current is 2*10^-5A...whereas with series combination it is 1.999999998*10^-5A...

but what is the conclusion in reference to the problem...?
I believe I see what he is getting at, but I think my response more directly addresses your question.
 
phinds said:
I believe I see what he is getting at, but I think my response more directly addresses your question.
can you please conclude...the problem...i am really stuck...
 
brainbaby said:
can you please conclude...the problem...i am really stuck...
I think I answered it completely already. Did you not understand my first post?
 
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phinds said:
I think I answered it completely already. Did you not understand my first post?
but in your first post current still seem to be dependent on both resistances...i am asking thst would it be possible to make current independent to anyone resistance just by increasing the other resistance to a higher value...
 
brainbaby said:
but in your first post current still seem to be dependent on both resistances...i am asking thst would it be possible to make current independent to anyone resistance just by increasing the other resistance to a higher value...
And my solution shows clearly that the answer to that question is a resounding NO. You really need to study what I said.
 
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  • #10
phinds said:
And my solution shows clearly that the answer to that question is a resounding NO. You really need to study what I said.
OK...then what logic LvW is talking about
 
  • #11
brainbaby said:
OK...then what logic LvW is talking about
He is attempting, I believe, somewhat indirectly, go get you to arrive at the same conclusion I presented you with.
 
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  • #12
Yes, it is easy. Just make one of the resistors infinite.

We are doomed.
 
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  • #13
brainbaby said:
with 1megaohm individual resistor ...current is 2*10^-5A...whereas with series combination it is 1.999999998*10^-5A...

but what is the conclusion in reference to the problem...?

That's the trouble with calculators versus slide rules.

Mother Nature is analog.

If you can discern the difference between those two currents with any real measuring device ,,,,

So -
As an engineer , to how many significant digits do you wish to push the question ?
As a mathematician, how would you describe the behavior of the limit as one of the individual resistors approaches infinity ?
 
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