# Calculus and a capacitor question

• posted

This is about the equation: C = I* dT/dE. I've taken Calculus and currently taking Diff EQ. At the moment I understand about applying Diff EQ techniques to turn that equation into a solution for all values of t (time). What does the equation mean in the form it's currently in? I understand the d means "instantaneous", however, I'm use to seeing equations such as: x d/dx and that tells me to differentiate 'x' with respect to x and the answer would be '1' (X^n = n * times X^n-1). Does the capacitor equation state: C = (I * T) d/dE ? if that's the case, the derivative would be 0 and the equation would C = 0. Theoretically it can be said that dT/dE means: (t1-t2) / (E1 - E2). Typically you can say that, but theoretically Calculus should be applied and I'm a bit confused about that equation. The inductor equation is another one that confuses me, however, I'm sure it would make sense once I understand the above.

• posted

Perhaps you're difficulty arises from having a transposed equation?

In its original form, it reads I = C * dV/dT, where dV/dT is no longer a quotient that can be split into two separate terms, but a function that results from the limiting process of reducing a time difference to an infinitesimal amount.

In its original form, it means that the instantaneous current, I, flowing into a capacitor, C, is proportional to the instantaneous rate-of-change of the voltage across the capacitor.

In the transposed form that you presented, C = I * dT/dV, it means that you can calculate the capacitance if you can simultaneously measure the current and rate-of-change of voltage. Your wish to express the time difference as (t1 - t2) and the change of voltage as (v1 - v2) would only be valid in the extremely simple case of a constant current and a linear rise of voltage.

(It would certainly be a true use of the facts, but the exercise I think you're undertaking is trying to understand the application of calculus, and whereas the use of a straight line is part of the derivation of calculus, it is only the derivation and once the limiting process of infinitesimal time has been applied the intention is that you should then work in a continuously changing world and not a world of straight lines that you are trying to go back to.

By all means revert back to the straight line derivation of calculus to remind you what's going on, but don't stay trapped in there when trying to use calculus.

PolyTech Forum website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.