Electronic circuits use various parts: resistors, capacitors, inductors, diodes, transistors, batteries, transformers, etc., and in most cases their operation can be understood by evaluating the voltages and electric current across/through the various parts. We use schematics (diagrams consisting of special symbols) to show how the parts are connected, and we use mathematical models (groups of equations) to calculate, predict, and analyze the circuits’ operation.

Some electrical/electronic circuits are so simple that they can be represented by simple schematics with equally simple mathematical models, such as this circuit:

This circuit is very popular, and is used in innumerable “flameless” candles all around the world. Starting from the left and going clockwise, we have a battery (BT1) rated at 3 volts, a power switch (SW1), and a yellow LED (a Light-Emitting Diode, labeled D1) which lights up when the switch is turned on (in the schematic above, the switch is shown in the “off” (or “open”) position. Between all of these elements are dark green lines that represent connections between the different parts. These tend to make us think of wires, but they may be direct connections, connections made up of copper lines (traces) on a printed circuit board (PCB), or some other method of connection.

Operation of the circuit is probably pretty obvious: turn on the switch, and the light goes on; turn off the switch, and the light goes off. Let’s see why: