Hello /sci/entists, I'm hoping you can help me refine an idea I have.

In my physics class we are studying electrodynamics, and recently we have learned to solve simple circuits of resistors. I'm sure you are familiar with this concept: you use the properties of conservation of energy, Vtotal = V1R1 + V2R2, Itotal = I1 + I2, and so on. You can then arrive at a system of equations for the unknowns you are trying to solve for.

Here is my idea: let's say we had a circuit where we could vary the resistance using rheostats, or change the connections between points using switches. If we measured the current at different points, we would have the solution to the derived system of linear equations above. Therefore, wouldn't it be possible to build a machine which solves systems of linear equations, just using a power supply, variable resistors, and a way to measure current? And if you had a large amount of resistors, you would be able to solve large linear equations instantly.

Note that I'm not saying this is a novel idea or terribly useful, considering we already have general-purpose computers which can do this kind of thing. I just think it would be something fun for a novice like me to build.