Hi for a project I am doing, it would be useful to measure voltage fluctuations in the microvolt/nanovolt area. The scenario is the following. I have a voltage divider circuit set up with R1 being a 4 ohm resistor and R2 being a 5cm pure silver foil with dimensions 5cm length and 1cm width(presumable having a resistance in the milliohms range). These R1 and R2 are connected in series using jumper wires in the breadboard. So I am taking the Vout from this divider i.e the drop across the silver foil(R2)(I know the jumper wire resistance will contribute to this drop as well) and then amplifying it using an opamp set to 100 gain.
The Arduino ADC gives an output, visualized with the serial monitor.

When the silver foil will be mixed with some chemicals, its electrical properties will change slightly and hence its conductiivity as well. I am only interested in measuring the difference i.e voltage drop across silver foil before solution mixed and after solution mixed (does not have to be accurate). Is the current method I am using valid? Can I measure nanovolt differences using this method. Is there any other more effective and reliable methods of measuring differences with nanovolt resolution?

If you know the thickness of the foil, you can calculate the resistance of your strip from the bulk resistivity of the metal - that would be very useful.

And do you really mean silver ? Ag ? or aluminium - cooking foil ?

At these very low resistance values you should use Kelvin connections for measuring the voltage drop - the resistance of the connecting wires will be significant.

And if you're etching the foil with highly ionic chemicals any contamination of the connections will set up galvanic voltages which could be much bigger than the small voltage you're trying to measure .

In such a scenario you may be better delivering an ac current and measuring an ac voltage - this also deals with the problem of removing the input voltage offset of the amplifiers you use.

ie if you have a voltage drop across the foil of a few mV and the input offset of the opamp is +/- 3mv, with a temperature coefficient of so many ppm/degree, what does your measurement mean?
not a trivial problem...

But start by finding out your foil material and thickness and go from there..

This is actually not recommended in a single stage amplifier. For reasons that are too technical to explain to an electronics newbie, it is best to use multiple amplifier stages of 50 or less, to obtain hich gain. (ie 10 x 10, or 2 x 25 , or 3 x 33 , etc etc etc.)

If you really need accuracy you can use an ic designed for precision:

nikhiljacob123:
So I am taking the Vout from this divider i.e the drop across the silver foil(R2)(I know the jumper wire resistance will contribute to this drop as well) and then amplifying it using an opamp set to 100 gain.

I would suggest that a breadboard is not suitable for this even using kelvin connections.

Needs to be soldered or clamped connections.

As raschemmel suggested go for an instrumentation amplifier, all the hard work has been done for you.

I am only interested in measuring the difference i.e voltage drop across silver foil before solution mixed and after solution mixed (does not have to be accurate). Is the current method I am using valid? Can I measure nanovolt differences using this method. Is there any other more effective and reliable methods of measuring differences with nanovolt resolution?

In all honesty, based on the nature of your questions, it is unlikely that you will be able to measure nanovolt differences.

Let's do the math:

1 nanovolt = 1V/1E-9 (that's one BILLION) =0.000000001 V

After your x100 amplifier,
0.000000001V * 100 =0.0000001 V (100 nV)

The 16-BIT ADS1115 has a resolution of 5V/65536 = 0.00007629 V/(per count) (that's 76.2 uV/per count)

that means that the 100 nV output of your x100 amplifier is 762.9 times SMALLER than the SMALLEST measurement capable with the ADS1115.

You might as well be in another universe. Obviously such measurements are possible but the question we need to be asking is are they possible by you with your current line of thinking .

I did the math and by my calculations you need a gain of 1000 JUST to be able to measure 1 nV.

If your gain was 1000 then 1 nV would be amplified to 0.00000076293 V (762.9 nV)

Let me put that another way,
If we arbitrarily say that we want to know the gain needed to amplify 1 nV to 2.5V, (2.5/1.0E-9),
then the answer is 25000000000 (25 BILLION)

What is the chance that you are going to come up with a circuit with a gain of 25 billion ?

If I have understand right he seems more interested in differences in order of nV (or more realistic uV) between the before and after the treatment. So this move away the needs of iper strong amplification, but not the one of the reference : AFAIK it' real hard finding a reference stable to single uV, and circuit layout not trivial at all. So I think it's a real hard job...

I think the point is that no matter what he is interested in it is impossible for a non-professional to detect any differences in anything that small.
Even if you reduce the gain requirements from 25 BILLION to 1 MILLION (25000 times smaller), that's still going to be a challenge.
How many amplifiers have you made with a gain of 1 MILLION ?

The only sensible way to measure a low resistance like that is with a precision high current pulse and kelvin
connections - and you'd have to measure / compensate for temperature too is the accuracy requirement
(in terms of %age change in resistance) is stringent.

Also I don't understand how a piece of foil can be "mixed with chemicals" and remain a piece of foil.
Exposed to chemicals yes, but not mixed.

When measuring such low voltages, one has to also realize
that every junction is a potential thermocouple.
careful thermal design is part of the problem.
The most sensitive way to measure is with a bridge. It is
much easier to measure current small current than voltage.
Look up electrometer.
Dwight

When the silver foil will be mixed with some chemicals, its electrical properties will change slightly and hence its conductiivity as well. I am only interested in measuring the difference i.e voltage drop across silver foil before solution mixed and after solution mixed (does not have to be accurate). Is the current method I am using valid? Can I measure nanovolt differences using this method. Is there any other more effective and reliable methods of measuring differences with nanovolt resolution?