# Calculate the resolution to measuring a range of resistances

Joined Sep 22, 2016
13
Hello, I have made a strange project i think its final purpose is not relevant so i will keep it simple. I want to measure the resistance (R2) by measuring the voltage drop across it and the current that is flowing through it. Now, i want to determine what is the resolution i need of both meters to determine to be able to distinguish between all R2 values i will have to measure. Their values i will be addressed shortly.

So the circuit simplified is the following: The voltage source puts around 1.2V, the R1 range is [97 to 27052] and R2[ 15- 9000].
The trick part comes now, when one resistor varies the other varies too. And i don't need the same R2 resolution across all range, for instance, the difference between the first 2 resistors i want to measure is 500 ohms and between the last two is 0.13 ohms.
To make it easier to understand i made a table of the R2 values i want to measure and its corresponding value R1:

What i would like to know, is how can i determine the resolution of my voltmeter and ammeter to distinguish the between all R2 values. Thank you

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#### crutschow

Joined Mar 14, 2008
23,312
The resistor resolution is basically the combination of the two meter resolutions.
Or do you mean accuracy, which is related but different?

How close resistor values do you want to distinguish?

#### BR-549

Joined Sep 22, 2013
4,936
Not sure what you're getting at.

Why not eliminate R1 and use a current source?

Joined Sep 22, 2016
13
The resistor resolution is basically the combination of the two meter resolutions.
Or do you mean accuracy, which is related but different?

How close resistor values do you want to distinguish?
No, i'm talking about the resolution. The thing is that i want to go the other way around, i want to calculate the resolution to explain my meters resolution choice.

Not sure what you're getting at.

Why not eliminate R1 and use a current source?
I know but i can't change. The point of my topic is how to determine the resolution i need to make the measurements, even if the approach is not the most correct or simplest

#### BR-549

Joined Sep 22, 2013
4,936
OK....then the max res will be the total of the max resistance you are using PLUS the max difference will want to be able to measure. 2 decimal places would be sufficient I would think........unless your secret project requires more.

Joined Sep 22, 2016
13
OK....then the max res will be the total of the max resistance you are using PLUS the max difference will want to be able to measure. 2 decimal places would be sufficient I would think........unless your secret project requires more.
what do you mean with the total of the max resistance ? sorry, but english is not my native language.

#### BR-549

Joined Sep 22, 2013
4,936
Let's say that you want to measure the value, AND THE DIFFERENCE in value of a group of resistors that range from 1 ohm to 99 ohms.

The max resistance is 99 ohms. That's two decimals to the LEFT of the decimal point.

Now for the difference........let's say you want to be able to tell one tenth of an ohm........that's one decimal to the right of the decimal point.

SO......two to the left and one to the right equals 3 significant places of resolution. 00.0 ..... If you just need the 1 ohm difference..........then 00 ..... 2 significant figures.

For a 1 meg resistor........000000.0 ...... 7 significant figures.

So.......it depends on the max resistance..........AND the difference that you need to know.

You have given the range of resistances.......but not the differences......and whether the difference changes, with the range of resistance.

I suspect that you might consider changing the resolution with the resistance range.

#### WBahn

Joined Mar 31, 2012
24,686
To be sure that I understand your objective, let's put it in a practical context.

You are given this list of R1,R2 resistor pairs. Then you are presented with the test setup you describe and based on a single measurement from the voltmeter and ammeter you need to be able to determine which of the R1,R2 pairs is currently in place.

If so, we can continue discussing how to choose adequate meters. If not, please explain in detail what you are expected to do (and how you are expected to do it).

Joined Sep 22, 2016
13
Let's say that you want to measure the value, AND THE DIFFERENCE in value of a group of resistors that range from 1 ohm to 99 ohms.

The max resistance is 99 ohms. That's two decimals to the LEFT of the decimal point.

Now for the difference........let's say you want to be able to tell one tenth of an ohm........that's one decimal to the right of the decimal point.

SO......two to the left and one to the right equals 3 significant places of resolution. 00.0 ..... If you just need the 1 ohm difference..........then 00 ..... 2 significant figures.

For a 1 meg resistor........000000.0 ...... 7 significant figures.

So.......it depends on the max resistance..........AND the difference that you need to know.

You have given the range of resistances.......but not the differences......and whether the difference changes, with the range of resistance.

I suspect that you might consider changing the resolution with the resistance range.
I gave the differences, its in the first post but i will post it here again:

For instance in the first 2 R2 values, they have a difference of 500 ohms but last ( in the end of the list ) is 0.126 ohms. And i have two changing values for the same R, its making me a little confused. I was thinking maybe to calculate this way:
Picking the 2 last R2 values ( the minimum difference) , 15 ohms and 15.126 ohms, assume the current is a constant : 10.9mA and the voltage resolution is what i want to find out . So I if there is change of .126 ohms, this represents, as stated in the datasheet, a change of aprox 1.4mV.

Now, thinking that the voltage is constant and the current resolution is what i want to find out, the change of 0.126 ohms with a voltage of 0.165V would represent a change of 69uA.

Is this absurd?

To be sure that I understand your objective, let's put it in a practical context.

You are given this list of R1,R2 resistor pairs. Then you are presented with the test setup you describe and based on a single measurement from the voltmeter and ammeter you need to be able to determine which of the R1,R2 pairs is currently in place.

If so, we can continue discussing how to choose adequate meters. If not, please explain in detail what you are expected to do (and how you are expected to do it).
No, i just want to determine the R2 value. However, i cannot ignore the R1 matter because it will limit the load current of R2 and so the voltage drop across R2 . I just want o measure the current and voltage across R2, but the R1 will change the voltage and current values range and its difference between values of resistance i want to measure.

Also I know that i will only have to measure a certain values of R2. These values have a corresponding R1, as i stated in that list. Did i made it more clear ?

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#### BR-549

Joined Sep 22, 2013
4,936
I do not understand what you are doing. I'm out.

#### MrChips

Joined Oct 2, 2009
19,270
The Thread Started has opened the thread on the wrong premise. It is very important to state up front the nature of the measurement otherwise all responses will be to no avail.

Is this an electrical conductivity measurement?

Tell us exactly what you are measuring.

Joined Sep 22, 2016
13
The Thread Started has opened the thread on the wrong premise. It is very important to state up front the nature of the measurement otherwise all responses will be to no avail.

Is this an electrical conductivity measurement?

Tell us exactly what you are measuring.
That was not my intention. Yes it is, but i don't see how it helps. I didn't say it to keep it simple and keep it on my topic question. Nevertheless, if you think it is important, So basicly is 4 probe cell where R2 is the water resistance and R1 is the impedance (generated by the polarization electrodes) seen by the voltage source . So since i'm not in fact using a current source, the current and voltage drop across R2 depends on R1 which are both varying according to the conductivity. Again, i cannot change the circuit, so i just looking how to determine the resolution needed to measure my values of R2, knowing that both I and V are changing between steps.

#### WBahn

Joined Mar 31, 2012
24,686
The fractional uncertainty in the calculated resistance value is the Pythagorean sum of the fractional uncertainties in the voltage and the current.

Determine what the worst case (closest) fractional uncertainty between any two R2 values. That's your first limiting case to examine.

Since your ranges are changing, look at the uncertainty of your meter on the appropriate range and determine the fractional uncertainty for each measurement (voltage and current). You can determine the allows fractional uncertainty in the measurement of each R2 value by noting that your measurement needs to place you within the limits established by the geometric means of that R2 value and the one above it and one below it.

#### MrChips

Joined Oct 2, 2009
19,270
That was not my intention. Yes it is, but i don't see how it helps. I didn't say it to keep it simple and keep it on my topic question. Nevertheless, if you think it is important, So basicly is 4 probe cell where R2 is the water resistance and R1 is the impedance (generated by the polarization electrodes) seen by the voltage source . So since i'm not in fact using a current source, the current and voltage drop across R2 depends on R1 which are both varying according to the conductivity. Again, i cannot change the circuit, so i just looking how to determine the resolution needed to measure my values of R2, knowing that both I and V are changing between steps.
Thanks for the clarification. Can you post information or a link to the cell?

Your initial post is very typical where someone assumes that this is the right approach. I see this often when sensors are bridges, strain gauges or thermistors. The obvious solution always appears to be some kind of voltage divider circuit whereas there could be other solutions available.

I have done electrical conductivity measurements and my approach has been to use an RC oscillator and measure frequency using a microcontroller. It requires no additional components except for a single capacitor across two pins of a microcontroller. This results in the best resolution and dynamic range which is really what you are trying to achieve.