This time we use the principle of minimum power to determine what a circuit made of resistors actually does. Its ‘behavior’ is described by a functor sending circuits to linear relations between the potentials and currents at the input and output terminals. We call this the ‘black box’ functor, since it takes a circuit:
and puts a metaphorical ‘black box’ around it:
hiding the circuit’s internal details and letting us see only how it acts as viewed ‘from outside’.
For more, see the lecture notes here: