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Identifying series and parallel connections

  1. Nov 26, 2015 #1
    1. The problem statement, all variables and given/known data
    In the arrangement shown,find the equivalent capacitance between A and B.

    CA.png
    2. Relevant equations
    Capacitance in parallel
    ##C##=##C_1##+##C_2##


    3. The attempt at a solution
    Supplied solution says
    As,we can clearly see that ,capacitors 10μF and 20μF are connected between same points ##C## and ##B##(Parallel combination)
    z.png
    They can be replaced by a single capacitor of capacitance given by
    ##C##=10μF+20μF=30μF
    Thus circuit can be shown by (b).
    Now ,the capacitors 15μF and 30μF are arranged in a row(sweries combination)
    the equivalent capacitance is given by C such that
    ##\frac{1}{C}##=##\frac{1}{15}##+##\frac{1}{30}##=##10##μF
    What I did not understand is
    They can be replaced by a single capacitor of capacitance given by
    Why can't I replace them as fllows
    WHY.png
     
  2. jcsd
  3. Nov 26, 2015 #2

    gneill

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    Are you asking if there is a difference between these two?
    Fig1.png
    Electrically, no: There is no difference. You can arrange circuit components in any way you wish on paper, draw wires or components at angles, make wires long or short, have wires wander all over the page, etc., and it will make no difference to the circuit. What matters is the topology of the network (what connects to what).
     
  4. Nov 26, 2015 #3
    Can you please provide me easy tip for identifying which capacitors are in parallel connection and which are not?I can identify in simple cases but when it is complicated ,I can't.
     
  5. Nov 26, 2015 #4

    gneill

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    Parallel components share two nodes for their connections. Series components have one node that they share exclusively (no other connections at that junction).

    A simple visual aid for finding parallel components is to color each node a different color (that includes all the wiring that makes up a given node). Components that are in parallel will connect to the same two color pairs. An example from a recent thread involving simplifying a resistor network is demonstrative:

    Fig1.png

    All the resistors that connect to the same color pairs are in parallel. Note that all the horizontally drawn resistors have the color pair (Blue, Red), so they are all in parallel despite how complex the network appears.
     
  6. Nov 26, 2015 #5
    What is exact definition of node in context of circuits.
     
  7. Nov 26, 2015 #6

    gneill

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    You should check your course text or notes for an official definition.

    But in simple terms, a circuit node is a conducting "island" in a circuit that is all at the same potential with respect to some fixed reference. Typically it is a conductive path (wire) that two or more components connect to.
     
  8. Nov 26, 2015 #7
    Here component can be capacitor,resistance ,keys ,switch ,bulb etc?
     
  9. Nov 26, 2015 #8

    gneill

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    Resistors, capacitors, inductors, diodes,...: yes. Things like switches and keys: no.

    Switches and keys can serve to change the domain of a node by extending or curtailing the conductor-connected region, but they are not electronic components in the intended sense of the word. They physically change the circuit topology when they are operated.

    A (light) bulb is just a fancy name for a special purpose resistor :smile:
     
  10. Nov 26, 2015 #9
    What about batteries?
     
  11. Nov 26, 2015 #10
    Are (1) and 2 two different (separate)nodes?
    nodes.png
     
  12. Nov 26, 2015 #11
    Are 1,2,3,4,5,6,7,8 nodes?If yes ,are 1,2,3 three different (separate)nodes?are 5,6,7,8 four different (separate)nodes?
    n.png
     
  13. Nov 26, 2015 #12

    SammyS

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    In case gneill is busy.

    Everything in blue is part of the same node. It's all made of ideal conductor.

    Everything in red is part of the same node. - a node different from the blue node.
     
  14. Nov 26, 2015 #13

    gneill

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    No. They are both on the same wire path. Everything with the same color belongs to one node.


    edit: Ha! SammyS snuck in there while I was otherwise occupied :smile:
     
  15. Nov 27, 2015 #14
    Are 1,2,3,4,5,6,7,8 nodes?
     
  16. Nov 27, 2015 #15

    SammyS

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    No.

    In post #11:

    The entire blue wire constitutes a single node. Points 1, 2, and 3 are all located on this same node.

    Points 5, 6, 7, and 8 are located on the red node.

    Point 4 is on the yellow node.
     
  17. Nov 27, 2015 #16
    What about batteries?
     
  18. Nov 27, 2015 #17
    Are component 1,2,3 underlined in blue in series? I think yes because they share a common node as highlighted by pink circle.

    HIGHLITED.png
     
  19. Nov 27, 2015 #18

    gneill

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    Yes: batteries and other voltage sources, also current sources, are components.
     
  20. Nov 27, 2015 #19
    And please answer my post#17
     
  21. Nov 27, 2015 #20

    gneill

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    No they are not in series. A pair of components in series share a single node exclusively (all alone, with nothing else connected to that node: Just one wire each from two components). The red and blue nodes have a lot of component connections, not two. That section of wire "A" alone that you've identified has four components connected to it!

    Besides, those components were identified as being in parallel earlier in the thread. The only case where components can be both in series and in parallel is when there are only two components in the circuit. Then their connections will agree with both definitions:
    Fig2.PNG
     
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