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Engineering LibreTexts

2.3.2: The Parallel Connection

  • Page ID
    52891
  • Consider the generic layout of Figure 4.2.1 , each component represented by a box.

    clipboard_e11e0f20659a3feb2952dda7a8dffa2f2.png

    Figure 4.2.1 : A parallel configuration.

    Although it may be drawn oddly, there are only two common connection nodes in this configuration: one along the top and the other along the bottom (if you're having difficulty seeing the bottom node, simply slide box E to the right and then rotate it counterclockwise 180 degrees so that its bottom winds up on top). Each of these blocks is like a rung on a ladder. If we were to take a voltmeter and place it across any of these blocks, the meter would read the same voltage across each because the probes are always contacting the same two nodes (remember, ideally the connecting wires have negligible resistance). Thus, we come to the first observation of parallel circuits:

    \[\text{In a parallel connection the voltage is the same across each component.} \label{4.1}\]

    A more complex configuration is shown in Figure 4.2.2 . In this layout some elements are in series and some are in parallel. Only elements D and E are strictly in parallel here as they are the only two that connect to the same two nodes, and thus must see the same voltage. Items C and F might at first appear to be in parallel with them but upon closer inspection it should be noted that C and F are in series with each other. That is, C and F will split the voltage that D or E sees, in accordance with the voltage divider rule. In other words, it is not true that the voltage across C or across F must be the same as the voltage across D or E. The same can be said for items A and B.1

    clipboard_e22c45d1db4060e2571f2b40d3c0dab9f.png

    Figure 4.2.2 : A more complex configuration.

    References

    1What can be said is that the series combination of C and F together is in parallel with D which is, in turn, in parallel with E. This is the basic idea behind series-parallel networks, the theme of the next chapter.

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