## Introductory electronics 2: Kirchhoff’s Laws

For the rules of the game of circuit analysis, the two main fundamentals are Kirchhoff’s circuit laws, of which there are two. Namely:

1. Kirchhoff’s current law (KCL): We assume safely that charge is conserved in any circuit, that is the amount of electrons going in must equal the amount going out. Specifically, the sum of currents entering a given circuit node equals the sum of currents exiting it.
2. Kirchhoff’s voltage law (KVL): Since energy is conserved, we have the result that the sum of voltage drops around any circuit loop must equal zero (where we assume that a voltage gain is like a negative voltage drop). This must be true since if it weren’t and we had a net positive potential difference in a loop, any electron going around that loop would gradually accrue more and more energy with no energy input (the loop is just sitting there after all).

An illustration of KCL is the following (from Wikipedia):

At the node (which we usually denote by putting a big black dot to symbolize the junction connection), we have $\displaystyle i_2 + i_3 = i_1 + i_4$.

For an illustration of KVL (again, thanks Wikipedia):

By KVL, we have $\displaystyle v_1 + v_2 + v_3 - v_4 = 0 \Rightarrow v_4 = v_1 + v_2 + v_3$ where I wrote the voltage source as having a negative voltage drop.

Since I have talked about voltage sources yet, I’ll say that whenever you’re designing or building some circuit you’ll either start with some source (like the $\displaystyle 5 \ V$ and GND leads from some other project) or you’ll have some battery. Ground (or GND) is any node in the circuit where you choose to define $\displaystyle 0 \ V$. It’s your free choice where to place it, so we usually like to define it somewhere that makes sense and helps us as designers. Fore example, in the KVL circuit above I’d set node d to be $\displaystyle 0$ since that would force node a to be whatever the defined voltage of the source is. It’s fairly common, especially with digital electronics, to have GND just be the negative terminal of the source.