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Sorry if this question is stupid, but I can't find any answers for this online.

Physics websites show that capacitors charge and discharge exponentially. The discharging graphs of charge against time show a 'normal' exponential decay graph. However, the charging graphs don't look the same as other exponential growth graphs. Instead of the quite flat line then steep curve, it is a steep curve from 0 which levels off. Why is this?

When I reference 'normal' graphs I mean the ones at Wikipedia (http://en.wikipedia.org/wiki/Exponential_decay and http://en.wikipedia.org/wiki/Exponential_growth).

I understand the basics of physically how a capacitor charges and discharges, I just don't understand why the charging graph doesn't look like other exponential increase graphs. Is this just my lack of understanding of maths?

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The curves show a charging that is proportional to

$1-\mathrm{exp}(-t/\tau)$.

Essentially, you should flip the exponential decay graph upside down.

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I understand the basics of physically how a capacitor charges and discharges, I just don't understand why the charging graph doesn't look like other exponential increase graphs.

But you know, if you understand how a capacitor charges, that the capacitor voltage asymptotically approaches the (constant) source voltage.

In other words, one shouldn't expect the capacitor voltage to grow exponentially (unless the source voltage is is growing exponentially too), one should expect the change in voltage to decay exponentially; the capacitor voltage changes rapidly at first and then more slowly, approaching the final voltage ever more slowly.

If the voltage on the capacitor were to grow exponentially, the voltage would increase at a greater and greater rate which wouldn't fit with your understanding of how a capacitor charges.

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  • $\begingroup$ Exactly, I know that the V-t charging graph makes sense as it is and that an exponential growth wouldn't fit. What I don't understand is why the graph is described as 'exponential'. This is probably due to my lack of mathematical understanding. In my mind you can have exponential growth and exponential decay, but what your and Eoin's answers suggest to me is that you can have some other kind of relationship which while still exponential isn't a decay or growth graph? If that is the case, how would you describe this graphical relationship? $\endgroup$
    – user112925
    Commented Mar 31, 2016 at 13:18
  • $\begingroup$ Thanks for both your and Eoin's help, I have come to except the relationship is exponential, just not in the conventional growth/loss sense. $\endgroup$
    – user112925
    Commented Apr 1, 2016 at 22:22

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