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node_loop_meth

# node_loop_meth - Notes on the Node Method and the Loop...

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Notes on the Node Method and the Loop Method The steps in the node method are: 1. Identify one node as the ground node, so that by definition, the potential at the node is 0 V. You may choose any node as ground, but often a judicious choice will simplify things later on. If there is only one source, make the negative terminal of the source ground. If there are several sources, all with a common node, make that node ground. Otherwise, choose one source, and make one of its terminals (usually the negative terminal) ground. 2. Label the potential of each node. Of course the ground node is at 0 V. Most of the other nodes will be unknown. Label them as e 1 , e 2 , etc. For voltage sources, use the constitutive relation to label one of the nodes. For example, if the negative terminal is at ground, and the source has strength V 1 , then the positive terminal is at V 1 . If the negative terminal is at, say, e 2 , then the positive terminal is at V 1 + e 2 . Generally, this process will lead to a unique (but perhaps unknown) voltage at each node. Furthermore, Kirchhoff’s voltage law will be satisfied automatically for each loop. This process can fail in one situation: If any loop in the network consists of only voltage sources, then that loop will not satisfy KVL (unless the source strengths happen to sum to zero around the loop). Physically, such a situation would lead to infinite current ﬂow, and so should be avoided! 3. For each node with unknown potential, apply Kirchhoff’s Current Law. This will lead to an equation in the unknown node voltage. (The equation will also involve other nodes that are connected to the node of interest by other elements.) There is no need to apply KCL at nodes with known voltage. Indeed, such nodes are connected to voltage sources, and the constitutive relation of voltage sources gives no information about the current ﬂow through the source; hence, it adds no new information that would allow one to find the unknown node voltages.

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node_loop_meth - Notes on the Node Method and the Loop...

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