SimplifyingNetworks - The arrangement shown to the right...

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Simplifying Resistive and Capacitive Networks Any network made purely of resistors or of capacitors can theoretically be simplified down to a single equivalent value by replacing each valid series or parallel pair with the appropriate equivalent. It is assumed that you know resistors add in series and capacitors add in parallel, and that the product-over-sum combination applies to capacitors in series and resistors in parallel. To save space, a single symbol will be used to represent either one in the next two images. The major problem first encountered with simplifying networks is correctly identifying valid series or parallel pairs. A series pair has one element immediately after another with no branching in between. The pair shown to the right would be in series, even though it is bent, if only there were not a branch leading off from between them. A parallel pair has both pairs immediately connected at each end.
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Unformatted text preview: The arrangement shown to the right would be parallel, even though one of the elements is arranged diagonally, except none of the pairs of elements are connected directly to each other on both ends. There are also no series pairs here. You would have to start simplifying somewhere else in the network first. What follows is a succession of images showing the gradual simplification of a resistive network down to a single resistance. (The ohm symbols have been left off to make it easier.) You should study this until you clearly understand what has happened at each step. The two large dots are called terminals and they imply that the network can be plugged into a power supply or circuit at those points. All you need to understand about them is that they are each open ends, so the 2 Ω resistor is not parallel to the 6 Ω resistor. 5 1 3 10 4 2 6 6 3 10 4 2 6 2 10 4 2 6 12 4 2 6 3 2 6 11...
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