Hi! Current neural engineering PhD candidate here. Your question is one I had early on when learning about brain modeling.
Noninvasive EEG sensors measure the synchronous activity of millions of neurons. While circuit equivalents of individual neurons are a well established idea (see Hodgkin-Huxley models for an early example), this approach does not scale to models of the full brain. There is research into using neural mass or neural field models as generative models of EEG/MEG, but those are statistical models over larger volumes of brain.
The brain is not an electric circuit. It's more like a hydraulic or osmotic circuit. Thought is powered by tiny flows of sodium ions, not flows of electricity. Specifically, sodium diffuses in blood/water much faster than charge dissipates through brain tissue.
When a lot of sodium flows into a cell (a neuron fires) it creates a positive voltage difference across the cell membrane. The concentration of sodium ions floating in the extracellular space remain essentially constant (sodium rapidly flows in from the outside area) even as the charge inside the neuron rises.
So as the neuron is at the peak of its action potential it acts like a 70 mV voltage source relative to the outside of the body. The EEG measures that voltage. It's like holding up a flourescent light near a Tesla coil[1]- electrodes closest to the neuron see a higher voltage from it, because they're measuring the ratio of resistance between 1. The electrode and neuron, through the head, and 2. the resistance to reference ground through the EEG itself. Because the head has quite high resistance (~megaohm?) EEGs require some serious input impedance.
On average neurons spend ~1 out of every ~10,000 milliseconds firing. If you had ~100 electrodes and 1 million neurons, you could triangulate to mostly work out where every single neuron is when it fires. In a human brain, there are ~billion neurons per electrode, with ~100,000 firing at any one time. EEGs are only really picking up on coordinated groups of millions of neurons firing together. Inferring where the actual neurons are is inherently a blurry guess. It is possible, but afaik (and I am very lay) most visualizations only interpolate surface potentials. Implanted electrodes can locate individual neurons, which is incredibly cool.
