I'm looking for a circuit that produces an output voltage which represents the voltage between A-B compared to B-C here. IE if AB is 10V and BC is 1V, the output is 10V, and if AB is 10V and BC is 2V the output is 5V.
Essentially what I want is an output voltage that represents the resistance ratio between R1 and R2.
The absolute output values is not important, as long as I can derive the current value of R1 from the known values R1(cold) and R2.
The reason is that R1 will change value as it warms, and I want to track that with a microcontroller. V1 will vary too fast to sample A and B separately, but I can use a single channel differential ADC if required.
I don't think this is possible without a very complex circuit having gone through it this morning but I thought I would throw it out there in case I am missing something.
EDIT: Thanks for both answers (and thanks for the 3rd but I don't really understand your suggestions). Firstly I think I can see that the result for me is that 'no its not possible to do it the way I hoped'. IE bridge like resistor networks.
The op amp idea is nice and probably the closer to my aim as I wanted a mathematical approach, but the result is that high currents need to go through linear devices which will lose considerable power and produce considerable heat. Also during fault conditions (which I will encounter) I won't be able to clamp the 200Aish currents fast enough to protect the devices I think.
The multiplier approach is also nice as I didn't realise a multiplier could be configured to divide. This one is more practical I think - but I don't think I can use it as I suspect I need greater accuracy and stability than I can get from relatively standard components, and the cost as you say is high.
So the result seems to be that I need to find another way to do it. Its hard to know who to award this to because I think both answers are equally excellent. Any help 'choosing' the most stack exchange 'best' reply would be appreciated.
As for my problem, I guess its either a sample and hold (I was thinking a homebrew with a 4066), or I will search for the controller mentioned that does simultaneous conversion. None of the ADCs I have seen seem to sample and hold the Vref voltage at sample time which is a pity as it seems to me that if I could feed A into Vref, B into ADC in, and C to gnd, that would work perfectly. Any further comments on that would be great if anyone had them.
Edit2: Since no one has commented as to the 'best' answer I think I am going to choose the op amp one, because of the algebraic approach and principle behind it which is kind of what I wanted (even if I wanted a non active type). Thanks to both.