There is a great deal of psychological research that shows that human beings can only hold seven (7) items (plus or minus two items) in their short term memory.  You can probably remember a list of seven numbers or names, but not a list of fourteen.

        Here's a little memory exercise for you.  Click the button below to show a set of numbers.  They will appear for exactly five seconds in the space below.  Look at the numbers, and - after they disappear - write down your best recollection of the set of numbers.

• You probably didn't get all of them correct.   However, a history expert or a history buff would have no problems recalling all twelve because they would remember this sequence of numbers as three dates (1066, 1492, and 1776!) that were dates of important historical events
• The important point is that the history expert would be trying to remember only three items, not twelve, and her/his memory can handle three items easily. The history expert needs to handle only three items because those three items are groups of smaller items "chunked" together.
• The person who knows history and remembers those three dates will not overtax her/his short term memory.  Someone not familiar with those dates will probably not be able to remember what they view as twelve different single digit numbers.

• Herbert Simon (a Nobel laureate in economics) did some work with chess experts and novices.  He found that novices could only remember a board with about seven chess pieces on it (remembering position of the pieces).
• However, a chess master can usually remember an entire chess board. The reason the master does so well is that the master's memory is organized to recognize patterns (like 1492 in the history expert's memory) and the chess master can remember up to seven patterns and locations of the patterns on a chess board.
• When chess masters were given boards with randomly placed pieces, not placed in patterns commonly found during a game, they did not do any better than novices at remembering the board!

        There are numerous recurring patterns in electrical circuits.  If you are going to be an expert in electrical circuits you should be able to recognize those patterns.  Some of those patterns are

• Series and parallel combinations of elements, especially resistors.
• Voltage dividers, including frequency dependent ones.
• Basic operational amplifier configurations.

        The problems are in a separate problem section, but you can click here to go to that section - or you can continue and see an operational amplifier circuit that has some hidden sub-circuits you should be familiar with.

        Here is an operational amplifier circuit.  However, it contains a circuit you have seen before.  Click the red button to see the voltage divider embedded in this circuit.  The voltage divider will be highlighted as long as the button is depressed.  Remember, no current flows into the op-amp input terminals.

        If you want to analyze this circuit, you can start by using the voltage divider expression to determine the voltage at the non-inverting input to the op-amp.  Recognizing the voltage divider is the key to figuring out what this circuit does.

        The expert will be able to seepatterns even when the topology is changed slightly.  Here are two pairs of networks.  In each case, the circuit on the left is the same as the circuit to the right.  If you doubt that you can check  how current flows in each circuit.  Trace  it out and you will find that they are in  fact the same circuits.