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How to recognize series versus parallel paths in complex schematics

  1. Jul 13, 2012 #1
    i'm working on a packet that i need to finish immediately! quick responses would be appreciated! my question involves simplifying circuit problems. a complex circuit is shown, and it asks what the total resistance of the circuit is. i assumed that each wire coming from the junction represented its own branch of a parallel dc circuit, so i simplified the schematic in this way, but the calculation didn't support it. how do i know which aspects of the schematic will be parallel and which will be series?
  2. jcsd
  3. Jul 13, 2012 #2
    If 2-terminal elements in the circuit share both nodes, they are in parallel. If two 2-terminal elements share one node only between the 2 of then they are in series. You can lump components in a circuit to represent 1 lumped element. The more you start lumping, the more you can start combining complex arrangements into simpler series and parallel circuits.

    You just have to know what you are doing and be careful when you start lumping elements, and you need to keep track of the lumped elements new values.

    Once you have analyzed the circuit by lumping many elements, you can then work backwards with the currents and voltages you have found to find voltage and currents of each component within the lumped elements.
  4. Jul 13, 2012 #3

    jim hardy

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    This is where the plumbing analogy can be helpful.

    If the term "node" is unfamiliar to you,

    try these simple thoughts. After your brain beats a thought path into itself you'll be an old hand at it.

    Two things are in series IF:
    All the current that flows through one MUST flow through the other because there's noplace else it can go.
    When you hook two short water hoses together to make one long one you have placed the two hoses in series.

    Two things are in parallel IF:
    The voltage across one MUST be exactly the same as the voltage across the other because their ends are connected together by wires, and the current has a choice which way to go.
    If you hook two garden hoses to a single faucet with one of these things
    and put the other end of both hoses in the same bucket to fill it faster,
    you have placed the two hoses in parallel.

    Now - a node is where at least two circuit elements join together. That garden hose wye thingie in picture above would be a node because there's one way in and two ways out.

    If there's only one way in and one way out i don't call it a node but some people do. To me it's a splice.
    So in example above where the two hoses are in series, their junction i would not call a genuine node but a splice.
    Some book authors disagree.
    Back to plumbing analogy - to me a pipe coupling is a splice not a node, but a tee or cross or wye is a node.
    On electronic schematics there's sometimes a dot at end of a component and sometimes not. Count the wires attached to the dot and decide yourself whether it's a genuine node.

    I oversimplify to help get a concept across. Hope this helps you, but be careful - in educated circles one needs to use the conventional terminology lest he be not taken seriously, or worse, miscommunicate.
    In electrical circles a junction where three or more things intersect is a node, and in some books so is a 'splice' where only two things meet.

    Good luck !
  5. Jul 13, 2012 #4
    my professor had us color each node in a different color in our intro circuits class. Actually kinda helped lol

    if two components have the same two colors on both sides then they are in parallel since each color would represent the same potential difference.
  6. Jul 13, 2012 #5

    jim hardy

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    That'll work !
  7. Jul 14, 2012 #6


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    You need to look at every pair of resistors and calculate their equivalent where you can (whether they are two in series or two in parallel). When you have all those values worked out, you will have enough to identify new pairs of series or parallel elements and further reduce the circuit - and so on, till you have just one equivalent resistor.
    This system works for many circuits but won't do for circuits with 'triangles' (deltas) of resistors, which don't reduce as easily but, if you are dealing with elementary problems, 'they' are unlikely to present you with anything like that.
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