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Resistors in Parallel - why the 1/R?

Zs
Hello, Genuinely, I hope this finds you well.


The electrical lessons which I am working on from home are going down well, despite my dodgy diagrams and rather plain English.  They have actually been rolled out to more people which I'm pleased about.  Anyway,  and after each one I get some comments or questions.


in the last one, I covered calculations for resistors.  You know the one for resistors in Parallel which is 1/R = 1/ value of resistor1 + 1/ value of resistor 2 +... and so on...?


Well, one of our ladies has suggested that it would be nice to know the derivation of the 1/R aspect, why it is divided into 1. I expect she already knows because she is a most interesting physicist and I have no doubt her maths is superb.  OMS will have met her.  Good question though. 


Truth is, I'm not sure and I have always rather taken it for granted as something I learned. Care to enlighten me? ...all I can think of is Kirchoff but I would love your advice if you have some time.


Thank you, stay well eh?  

Zs


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  • 0
    Perhaps curiously, for I am an electronics guy at heart and do a lot with Rs and Cs in parallel and series, I have never considered there to be a special formula, though now I look around, indeed there it is.

    For things in parallel they all see the same voltage, so we just add the currents to get a total.

    For things in series, they all pass the same current, so we add the voltages.

    The when converting back to an equivalent single value of Z, as we only need a ratio of V to I,  the unknown voltage or current just cancels.

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  • 0
    Perhaps curiously, for I am an electronics guy at heart and do a lot with Rs and Cs in parallel and series, I have never considered there to be a special formula, though now I look around, indeed there it is.

    For things in parallel they all see the same voltage, so we just add the currents to get a total.

    For things in series, they all pass the same current, so we add the voltages.

    The when converting back to an equivalent single value of Z, as we only need a ratio of V to I,  the unknown voltage or current just cancels.

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