An electric circuit, from a microscopic point of view, is a monstrously complicated object: conduction electrons diffusing through a metal lattice, electric fields propagating in dielectrics, energy exchanges with lattice phonons. Yet to design your guitar amplifier it’s enough to write a few Kirchhoff equations and use five or six ideal components: resistor, capacitor, inductor, battery, transistor.
This drastic reduction is not free; it is the result of an abstraction built piece by piece in the nineteenth century. Kirchhoff understood that, at not-too-high frequencies, the electromagnetic field is “trapped” in the conductors and dielectrics, and that the energy exchanges can be accounted for as voltages and currents at the ends of a few nodes. Conservation of charge becomes the node law; conservation of energy (i.e. the existence of a potential) becomes the loop law. With these two laws and a handful of constitutive relations (, , ) one builds the whole of analogue electronics — at least until the wavelength becomes comparable to the size of the circuit (at GHz and beyond, where transmission lines and then the full Maxwell equations are needed).
It is a paradigmatic example of what “model” means in physics: deliberately discarding almost all of reality in order to keep in view the part that is relevant at a given scale. The strength of the model lies precisely in the courage to throw away.
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Topics: Electric circuits Skills: Limiting-case analysis and thought experiments
Related exercises: Worked exercise — mixed series-parallel network · Worked exercise — capacitor network · Worked exercise — charging RC circuit