1.3: Node Voltages and Reference

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Page ID: 55509

James Kirtley
Massachusetts Institute of Technology via MIT OpenCourseWare

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One of the consequences of KVL is that every node in a network will have a potential which is uniquely specified with respect to some other node. Thus, if we take one of the nodes in the network to be a reference, or datum, each of the other nodes will have a unique potential. The voltage across any network branch is then the difference between the potentials at the nodes to which the element is connected. The potential of a node is the sum of voltages encountered when traversing some path between that node and the datum node. Note that any path will do. If KVL is satisfied, all paths between each pair of nodes will yield the same potential.

A commonly used electric circuit is the Wheatstone Bridge, shown in its simplest form in Figure 8. The output voltage is found simply from the input voltage as just the difference between two voltage dividers:

\(\ v_{o}=v_{s}\left(\frac{R_{2}}{R_{1}+R_{2}}-\frac{R_{4}}{R_{3}+R_{4}}\right)\)

This circuit is used in situations in which one or more resistors varies with, say temperature or mechanical strain. The bridge can be balanced so that the output voltage is zero by adjusting one of the other resistors. Then relatively small variations in the sensing element can result in relatively big differences in the output voltage. If, for example R₂ is the sensing element, R₄ can be adjusted to balance the bridge.