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Can anyone help my 13 year-old with an assignment? I have little knowledge about electricity and I need to teach her about circuits. We have a question from her seventh grade science book that has us stumped. The chapter is titled "Electric Charges and Currents" and the section from which it comes is titled "Series and Parallel Circuits". The section gives a basic definition for a series circuit and a parallel circuit followed by several questions. The one we are stumped on is written exactly like this:

Can a circuit be a combination of series connections and parallel connections? Explain your answer.

Any examples would be appreciated.

textbook illustration of series circuit and parallel circuit

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schematic

simulate this circuit – Schematic created using CircuitLab

For this circuit, you can say that voltage across both the elements is the same. Current flowing through battery and the resistor is also the same.

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I'm not sure if this is a formal definition, but this works pretty well in practice:

  • If elements have the same current running through them (they share a voltage drop) they are in series.

  • If elements have the same voltage across them (they share current) they are in parallel.

Edit to answer newly updated question:

Yes, you can combine series and parallel elements:

schematic

simulate this circuit – Schematic created using CircuitLab

This is an example of both a series and a parallel connection in the same circuit. In this example, $$\text{Voltage D} - \text{Voltage F} = 10V\;\text{(due to the battery)}$$ and Voltage E is somewhere in between the two (the voltage is shared by Lamp 1 and the combination of Lamps 2&3).

You can also see that the Current A is being split by the elements Lamp 2 and Lamp 3, into Current B and Current C. Since we can't create or destroy current, they add up to Current A: $$\text{Current A} = \text{Current B}+\text{Current C}$$

So you can say that Lamp1 and the combination of Lamps 2&3 are in series (Lamp 1 and the combination of Lamps 2&3 have Current A in them), while the sub-circuit of Lamp 2 and Lamp 3 has a common voltage across those elements (\$\text{Voltage E}-\text{Voltage F}\$) so they are in parallel!

I've gone a little overboard on answering this question in a very general and mathematical way, but that's how people who do circuit design work with these numbers :) If anything is unclear, feel free to ask below.

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    \$\begingroup\$ Using a mathematians lens this would mean that a 2 element circuit is an example of a circuit both series and parallel as rules/laws associated with both symmetries will apply. However this somewhat of an abstraction as a real voltage source may likely physically be a multiple element net and really it's just a consequence of simplifying circuits into thevenin equivalents \$\endgroup\$
    – crasic
    Feb 4, 2016 at 6:22

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