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What is the fact of constant of proportionality? 
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#1
Jul109, 03:41 AM

P: 77

Its so confusing for me.....
in Ohm's law V=IR here V is independent variable and I is dependent variable (i,e increasing V, I also increases) here we place R (proportionality constant) with I (dependent variable). On the other hand.. in electrostatic force F=k(Qq/r^2 ) here K is constant of proportionality that is written with independent quantity. Here is also an example: Q=CV (Q is independent and V is dependent variable) here C (capacitance) is placed with V (dependent variable) Here is.... R=pL/A (rho is placed with independent quantity) Please tell me the actual fact of constant of proportionality. Thank you 


#2
Jul109, 04:01 AM

PF Gold
P: 7,120

There are a few things I can point out that hopefully makes this a bit clearer. When you have V = IR, you can easily flip that and say I = V/R thus switching where the "proportionality constant" is and the equation works just as well. Now the resistance is paired up with the independent variable. Another important thing is in this case, resistance is not really a proportionality constant in the way it's usually meant. You can in fact vary R so it is more of a parameter. Think of a rheostat. Ohm's law still holds even though you can vary your resistance.



#3
Jul109, 04:12 AM

P: 1,164

dependent and independent variables are in the eye of the beholder. Proportionality constants aren't variables at all. They're essentially constants put in to make the units work. In V=IR none of them are proportionality constants, they're all variables and whether one is independent or dependent depends on what is a function of what in your perspective. The constants of proportionality are things like k (in coloumb's law), kb (boltzmann's constant),etc. Basically these constants make up for the fact that our SI units don't really line up. For example, in coloumb's law we have a force that is a function of C/m^2. However, the unit we picked for force, the Newton, was chosen (and it was chosen, there's no ultimate reason for choosing what our unit of force should be) based on different ground and thus a unit charge (in our arbitrary units of charge) divided by the square of our chosen unit of distance does not correspond to a single unit of force, in our units. So we toss a constant in to "map" between our units.



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