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Throughout the labs and tutorials, you'll see circuits represented different ways. You might see photographs of a breadboard (insert photo), or a pictograph showing the breadboard components and wires (these are one of the views from Fritzing. (insert fritzing breadboard)
The standard way for documenting a circuit is called a schematic. A schematic uses a library of symbols representing electrical components, and lines showing how those components are connected.
Reading schematics isn't too hard - there are only a handful of components we'll need to remember for most of what we'd encounter in pcomp. However, it can take some getting used to the fact that the schematic layout might differ significantly from the physical layout of a circuit on a breadboard. A schematic is purely functional - as long as the proper components and connections are represented, their position in the diagram are of no significance. if it makes the diagram neater to move parts closer to one another that's fine.
Some of the most often encountered symbols in a schematic are: (picture of symbols here) A conductor (just a line) Power (various ways) Ground Resistor (wiggly line) Capacitor (two lines) Diode and LED Variable resistors (including potentiometers) Transistor (various, see NPN)
Component symbols will typically be accompanied by a value (e.g. 100k = 100 kilo ohms = 100,000 ohms) and maybe an ID (like R1 - "resistor 1"). More complex components might be represented simply as a rectangle with some number of pins, usually labeled in the schematic itself, or at least numbered for referring to the datasheet for that part. Some parts (e.g. amplifiers) are represented as triangles.
When two lines in a schematic cross, there are different conventions for depicting if that represents an electrical connection at the cross point. A dot at a cross indicates a connection, and a "hump" indicates no connection; some schematics use one and imply the other. (illustration)
To avoid lines going all over the place, common connections like ground and 5 volts are sometimes repeated wherever convenient, rather than drawn as literally connected. Except for rare circumstances, anything shown connected to ground is electrically connected, even if there are several ground symbols used throughout the schematic.
Good resource for more in-depth info on schematics is here: http://www.beavisaudio.com/techpages/SchematicToReality/