# Making the sum of 2 resistors independent of 1 of them

• brainbaby
In summary, LvW is trying to get me to come to the same conclusion that he did. However, I don't think that is what he was asking.
brainbaby
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

brainbaby said:
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.

davenn and brainbaby
Compare the current through a 1-Mega-Ohm resitor with the current drawn by a series combination of 1 Megohm and 1 Milliohm.

brainbaby
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?

davenn
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.

davenn
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

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.

davenn
Yes, it is easy. Just make one of the resistors infinite.

We are doomed.

brainbaby
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 ?

brainbaby

## 1. How can I make the sum of 2 resistors independent of 1 of them?

To make the sum of 2 resistors independent of 1 of them, you can use a voltage divider circuit. This involves placing a third resistor in series with the two resistors whose sum you want to make independent. The value of this third resistor can be calculated using the formula R3 = (R1 * R2) / (R1 + R2).

## 2. Why would I want to make the sum of 2 resistors independent of 1 of them?

There are several reasons why you may want to make the sum of 2 resistors independent of 1 of them. One common reason is to create a specific resistance value in a circuit. By varying the value of one resistor, you can adjust the overall resistance without changing the other resistor's value.

## 3. Can I use any combination of resistors to achieve independence?

No, not every combination of resistors will result in an independent sum. The two resistors must be in series, and the third resistor must be in parallel with one of the two. Additionally, the value of the third resistor must be carefully calculated to achieve the desired result.

## 4. Are there any limitations to this method?

While using a voltage divider circuit is a commonly used method to achieve independence, it does have some limitations. For example, the output voltage may vary depending on the load connected to the circuit. Additionally, the third resistor may introduce additional noise or power dissipation.

## 5. Are there any alternative methods for achieving independence?

Yes, there are alternative methods for making the sum of 2 resistors independent of 1 of them. One method is to use an op-amp circuit with negative feedback. This allows for precise control of the output voltage and can eliminate some of the limitations of the voltage divider circuit. However, this method may require more complex circuitry and additional components.

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