The category with linear circuits as its morphisms, labelled sets of electronic terminals as its objects, and laying circuits in parallel as the monoidal product (which is the usual notion of the category of circuits; perhaps you have something more sophisticated in mind, but if so you should specify that) is not cartesian closed.

One of the many ways to demonstrate this: all linear circuits have duals (voltage <-> current, series <-> parallel, and so on), but in a cartesian closed category only the terminal object is dualizable.

What you're probably thinking of is the fact that this category is compact closed. The corresponding internal language is going to be some sort of process calculus (I think the pi calculus is too strong, but not sure), not the lambda calculus.