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Basic question: is there a term defined for the difference in relation between two equations of the same proportionality? I've noticed this effect but haven't been able to find a word for it. I've always known proportionality to relate both expressions of an equation, and not a single expression.

For example: P = IV where P is power, I is current, and V is voltage

and V = IR where R is resistance.

As the resistance increases, the current decreases proportionally, keeping the voltage constant. Assuming a constant voltage supply is present, you may alter the resistance and the current changes inversely, yet they are both multiplied in the formula.

On the contrary, as the voltage increases in P = IV, the current does not decrease. It is well known that as the voltage increases, so does the current.

Thanks for your insight!

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  • $\begingroup$ I think this is pretty much saying: you can set $V$ and you can set $R$ but you can't set $P$ or $I$. And that's not entirely true either, for example in a real resistor $R$ depends on $V$. $\endgroup$
    – Ian
    Aug 15, 2017 at 14:27
  • $\begingroup$ Alright. So there isn't a term for this, tho? It seems strange that these two types of equations aren't separated. They operate very differently. $\endgroup$
    – ABC DEF
    Aug 15, 2017 at 14:29
  • $\begingroup$ I don't think there's a standard term, but one way to view it is that you have four variables and two equations, so mathematically you should be able to choose any two of the variables to be the independent variables and then the other two will follow. But in practice you can't set two of them as you see fit, so you don't have free choice of the independent variables as a practitioner. But again, that's not really entirely true: for instance, $R$ is not free to be set, it depends on the voltage in a real resistor rather than an ideal one. $\endgroup$
    – Ian
    Aug 15, 2017 at 14:32
  • $\begingroup$ (Cont.) Similarly at a power plant the independent variables are closer to being $P$ and $V$ than anything else. $\endgroup$
    – Ian
    Aug 15, 2017 at 14:34
  • $\begingroup$ I think dependent and independent are close enough to what I am looking for. They describe the variables rather than the equation. Thank you! $\endgroup$
    – ABC DEF
    Aug 15, 2017 at 14:39

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