By John E Whitehouse
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Additional resources for Circuit Analysis
Further, as a non-planar graph has no unique represen tation, so it and its associated circuit have no unique dual. Duality is therefore confined to planar circuits. 15 Summary The principle of superposition, which formally underpins the linearity of systems, has been re-examined, on this occasion in regard to its usefulness in analyzing networks where more than one source is present. A partial solution for a network, the voltage across a single branch or the current in such a branch, can be found by adding the effects of each source with all the other sources suppressed.
In each, one source has been suppressed. The combination of resistors in parallel is required in each case followed by the treatment of each network as a potential divider. The result is 3 V for (b) and 6 V for (c) giving a total of 9 V for VAB- When there are both independent voltage and current sources present in a network it is often useful to perform source transformations so that only voltage sources remain, in a case where a net voltage is required, or so that only current sources remain, where a net current is required.
Thevenin's theorem is central to the theme of network analysis and it is appro priate to illustrate it with a number of examples. 7). The Thevenin equivalent voltage (vjh) is that which appears at the output terminals of the network when open-circuited. 8) pro vides a useful illustration. The temptation is to suppress the source and attempt to find the effective resistance in one move, which is algebraically cumbersome. 8(b) to (d)), reducing each potential divider in turn. The particular set of resistor values chosen for the example ensures that the Thevenin voltage is halved at each stage (a binary sequence).