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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
    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

    If it helps at all, I think of resistors in parallel means that the currents through each of the resistors simply add up to the total. Current through each individual resistor is inversely proportional it's resistance - as R increases I decreases (1/R).


    Or if you want to think of it all mathematically, the current for the whole lot Itotal = the sum of the currents through each of the resistors I1 + I2 etc.


    Remembering that I=V/R, that's the same as saying:


    Vtotal/Rtotal = V1/R1 + V2/R2 etc


    But as all the resistors have their connections in common, all the voltages are the same, so we can cancel them out, which leaves us with:


    1/Rtotal = 1/R1 + 1/R2 etc.


    With resistors in series the resistance simply add up and it's the voltages across them that are proportional to their individual resistances.


    Does that help at all?


       -  Andy.
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  • 0
    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

    If it helps at all, I think of resistors in parallel means that the currents through each of the resistors simply add up to the total. Current through each individual resistor is inversely proportional it's resistance - as R increases I decreases (1/R).


    Or if you want to think of it all mathematically, the current for the whole lot Itotal = the sum of the currents through each of the resistors I1 + I2 etc.


    Remembering that I=V/R, that's the same as saying:


    Vtotal/Rtotal = V1/R1 + V2/R2 etc


    But as all the resistors have their connections in common, all the voltages are the same, so we can cancel them out, which leaves us with:


    1/Rtotal = 1/R1 + 1/R2 etc.


    With resistors in series the resistance simply add up and it's the voltages across them that are proportional to their individual resistances.


    Does that help at all?


       -  Andy.
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