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Resistance and capacitance (of parallel plate capacitors) both have two formulas for them: $R=V/I$ and $R=ρL/A$ for resistance, and $C=Q/V$ and $C=ƐA/d$ for capacitance. For any given resistor and capacitor with given dimensions, there is only one possible value of resistance or capacitance calculated using the second formulas (formulas with variables of dimensions of the component). However, depending on the potential difference across the components and many other variables (e.g., current for resistance and charge on the plates for capacitance), it seems like a given component can have many resistance or capacitance values different from the value given by the formulas considering the dimensions of the component.

So, my question is: What is the difference between the two formulas for each of resistance and capacitance? Under what circumstances is one formula more applicable than the other?

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  • $\begingroup$ There do exist, for example, materials that do not have constant resistance (like light bulb filaments due to temperature changes). Is this what you are asking about? $\endgroup$ – BioPhysicist Mar 25 at 2:00
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For an Ohmic resistor, the second equation applies. Similarly for a parallel plate capacitor. $V$ and $I$ or $V$ and $Q$ will have a set relationship; that cannot be varied independently for the given circuit element.

However, your first equations apply more generally for any system. i.e. if you take something (doesn't need to be Ohmic) and apply a voltage drop $V$ and get a current $I$, then the resistance (at the moment) is $V/I$.

Similarly, for a capacitor (doesn't need to be a parallel plate capacitor), if you apply a potential difference $V$ and you get a charge separation $Q$, the capacitance is $Q/V$.

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  • $\begingroup$ Oh okay. So, Ohmic resistors have constant resistance given by the second equation, and the first equation will hold accordingly, and thus the V vs. I graph has a constant gradient. But then for non-Ohmic resistors, R=V/I is more useful to find the resistance at certain given potential difference and current. Is there any similar comparison for capacitors like the comparison between Ohmic and non-Ohmic devices for resistors? $\endgroup$ – Donghwi Min Mar 25 at 2:10
  • $\begingroup$ @DonghwiMin You got it! For capacitors I'm guessing similar behavior could occur if the dielectric properties changed for different applied voltages so you would have $\epsilon=\epsilon(V)$ (assuming a constant geometry). $\endgroup$ – BioPhysicist Mar 25 at 2:34

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