Control theory: What is the relationship between the number of elements in your system, and your diff'eq IO model and the dimension ABCD Matrix?
Assume your circuit can be described as a set of linear first order differential equations, and that it is a single input, single output (SISO) system. With this assumption the system can be written in a state space form as:

$$\dot x = Ax + Bu$$

and

$$y = Cx + Du$$

where x is the state vector, u is the input, and y is the output. A is the 'system' matrix that determines the dynamics of your electrical circuit. B is the input coupling vector. It determines how the input is coupled to your set of state equations. C is your output coupling vector, and it determines how the system states are coupled to the otput. Finally D is your feedforward coupling factor (a scalar) that determines how (or if) the input is directly coupled to the output without dynamics.

Now to answer your question. By expressing your circuit in terms of a finite set of N linear first order differential equations you you are said to have an N-state system, and A will be N X N, B will be N X 1, C will be 1 X N and D will be dimension 1.

The system dimension is not equal to the number of elements or to the number of energy storing elements (e.g. Capacitors and Inductors) but rather the minimal number of first order linear differential equations that can describe the system. Another way to figure this is to write any set of differential equations to describe the system and count the number of integrators (not differentiators). That will give you the order (dimension) of the system.

The same reasoning can be applied to a MIMO (multi input, multi output) linear state space system where B, C are more generally matrices.