For the most part, the circuits we’ve encountered have been either series or parallel circuits with no deviance from either extreme. The only exception to this trend regarded circuits that had multiple voltage sources positioned within their multi-loop matrix. Adding to this complexity was the fact that these voltage sources could be oriented in any way whatsoever. Analysis of such circuits required usage of Kirchhoff’s voltage and junction rules to determine the direction of current flow within the circuit’s branches. We will now begin to study circuits in which single voltage sources ( Vs ) supply current to circuits that have both series and parallel components. First, let’s review the basic structure of a simple series and parallel circuit, both of which contain three resistors ( R ):
Simple Series Circuit:
Simple Parallel Circuit:
Please recall how resistors in series with one another have a common flow of electrical current ( I ) through them. For this reason, we can easily establish a series-parallel circuit by placing a resistor along any of the branches of the parallel circuit as follows:
We now have a circumstance in which the R4 resistor is in series with the R1, R2 , and R3 circuit elements, all of which reside on different branches. Resistors could just as easily be placed elsewhere to establish a valid series-parallel relationship within the circuitry. It would be wise to practice drawing additional circuits by placing one or more resistors along the other circuit branches prior to seeing how series-parallel problems are analyzed and solved.
RENAISSANCE PHYSICS 