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We can solve for 2-node cases by hand. Some cases and their solutions are given here. These can be useful for understanding how GUNNS effects behave, such as capacitance, conductance, etc. We won’t give all the algebra, but it can all be derived by building the [A]{p} = {w} system of equations and solving for {p} by hand.

Here we have two nodes given capacitance C ₁ and C ₂, respectively, connected by a conductor with admittance A:

This is same as Case 1 but we add a flow source F onto Node 2.

This is the same as Case 2 but we’ve replaced the flow source with a potential source with admittance A _e and source potential P _e.

This is the same as Case 1 except we’ve replaced the conductor with a potential source with admittance A and source potential P.

This is the same as Case 1 except Node 2 is non-capacitive. This is a trivial case: no matter what the starting potentials P _1,0 and P _2,0 are, since Node 2 has no capacitance, it cannot receive any flow from Node 1, there is no flow through A, Node 1 keeps the same quantity and therefore potential, and the Node 2 potential is always equal to Node 1.

This is the same as Case 2 except Node 2 is non-capacitive. Note the solution for P ₂: it clearly shows the behavior of a conductor, i.e. V = IR, where R = 1/A, I = F, V = dP = P ₂ – P ₁.

This is the same as Case 3 except Node 2 is non-capacitive.