INTRODUCTION TO ELECTRONICS: Series-Parallel Circuit Branch Identification

Due to the complexity of some series-parallel circuits, it takes time to appropriately identify circuit branches that negate the larger circuit being classified as purely series or parallel. There is no substitute for practice! Prior to using the appropriate mathematics and equations to solve series-parallel circuit problems, visual engagement with a wide variety of circuit types is crucial. We will begin practicing with a relatively simple circuit with subsequent circuits being slightly more complex:

Within series circuits, the full quantity of electrons leaving the source pass through every resistor ( R ) along the path. Resistor R₁, has the full quantity of current ( I ) passing through it; however, R₂ and R₃ are preceded by a node that splits the current apart:

Although this diagram is very basic, it constitutes the general structure of series-parallel circuits that will be encountered. The diagrams that follow simply add resistors to the branches that are present:

In the absence of R₃, we would have a series circuit. Notice also that R₃ is now parallel to a circuit in which R₂ and R₅ are in series. All of the aforementioned resistors are downstream of a node, and preceding this node is yet another series circuit composed of R₄ and R₁. 

We must now address an important question: How would such a circuit’s total resistance value be determined? There’s no particular order in which resistors should be combined, but we must be sure that the equations used are appropriate. If we add R₂ and R₅ together, we have an equivalent resistor that can be added to R₃ via usage of the double reciprocal formula. Afterward, we will have a resistance value that can be added to the branch containing R₄ and R₁. In our last diagram, a sixth resistor is added in parallel to the series branch containing R₄ and R₁:

This lattermost circuit can be solved using the same techniques as beforehand. This time around, we may choose to add R₄ and R₁ together and add their sum to R₆ via the double reciprocal method. We would then have a single resistor value upstream of the first node. The resistors downstream of the node would then be added together, and their sum added to the resistor value of the first branch.