1. The problem statement, all variables and given/known data In the Lectures, we are told that techniques like homogeneity and superposition work only for linear circuits, but in Chapter 3 of the Textbook (which is the only place I can find one) I see a definition of linearity as "A circuit is linear if and only if 2. Relevant equations f(ax1 + bx2) = af(x1) + bf(x2)" i.e. if homogeneity and superposition work for it. 3. The attempt at a solution How do I tell, when confronted with an arbitrary circuit, whether or not it is linear - whether or not homogeneity and superposition are going to work for it?
No circuit is purely linear. Even R's and C's have voltage-varying i-V characteristics. Obviously, a linear model works very well in almost all instances. Transistor circuits are less linear: usually a linear approximation is made, like an equivalent circuit, constant beta, zero di/dV_{ce} in the linear mode, etc. Diodes are clearly non-linear, since they conduct in one direction but not the other. Zeners are in the same category: their i-V relationships are highly non-linear. Photodiodes are amazingly linear, providing nearly constant di/dI over as many as 5 orders of magnitude (100,000 to 1). I = intensity. Got any other devices in mind?
This apply only with LINEAR ELEMENTS in circuit. In fact, only independent sources, linear-dependent sources and resistors are allowed.