# The Art of Electronics (Integrators)

Reading this topic from "The Art of Electronics" : Integrators

How does RC keep V << Vin?

• It is not a matter of RC keeping ("forcing") V << Vin. You should interpret this as: RC should be large, then when V << Vin we can use the formula. If RC is small and/or V isn't much smaller than Vin, we cannot use the formula. – Bimpelrekkie Mar 18 '19 at 12:34
• It doesn't say RC keeps V << Vin. It says "we" keep it this way. – Dmitry Grigoryev Mar 18 '19 at 12:41
• For those without access to the text the OP refers to, the fuller context can be read here at the end of page 26 of the older 2nd edition. – jonk Mar 18 '19 at 19:33
• To the OP: All that's being said here is that if you can arrange things so that the capacitor stays relatively uncharged, then the charging current will closely approximate a constant. If, on the other hand, you allow the capacitor to charge "for a long enough while" then the magnitude of the current will be seen to change over time and can't be considered a constant, anymore. In that case, you wind up with no longer a constant but instead a continually varying current and, ultimately, it involves exponentials/logarithms and stuff gets more complicated. – jonk Mar 18 '19 at 19:37

If $$\RC\$$ is very large, current is very small, $$\\frac{dV}{dt}\$$ goes to zero, thus $$\V\$$ does not change.