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I read that the formula for calculating the time for a capacitor to charge with constant voltage is 5·τ = 5·(R·C) which is derived from the natural logarithm.

In another book I read that if you charged a capacitor with a constant current, the voltage would increase linear with time. Is this true, and if it is, what is the formula used for calculating this? Would a complete voltage charge be possible with a constant current?

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    \$\begingroup\$ To achieve a constant current through a capacitor implies that the voltage across the capacitor increases without limit. In reality, "without limit" is limited by the capacitor exploding. 5 tau is generally taken to be "good enough" at 99.3% charged. \$\endgroup\$
    – Andrew Morton
    Commented Nov 20, 2016 at 18:28
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    \$\begingroup\$ A real constant current source such as a LM334 will "drop out" at its lower compliance limit and tail the charge current off as a result when the cap's fully charged up, provided the cap is rated well enough to not go bang first. \$\endgroup\$
    – ThreePhaseEel
    Commented Nov 20, 2016 at 18:31

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Normally I would let you go and look as this is not a hard question to solve, but as I am feeling generous here is how we get there:

From fundamentals, we know that \$Q =CV\$

If we take the derivative with respect to time (remembering that \$I = \frac {Q} {T}\$) we yield

\$i = C\frac {dv} {dt}\$

Rearranging, we find that \$\frac {i} {C} = \frac {dv} {dt}\$

Therefore charging a capacitor from a constant current yields a linear ramp (up to the compliance of the current source).

I will leave finding the solution in terms of time versus some voltage to you.

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    \$\begingroup\$ charge time = C x V/I \$\endgroup\$
    – mrbean
    Commented Jan 27, 2023 at 17:32
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Here is the equation:

charge time = C x V/I

A good read: https://www.us.lambda.tdk.com/resources/blogs/202106.html

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    \$\begingroup\$ This should be the accepted answer. Rather than the pompous reply which stops short of actually answering the question. \$\endgroup\$
    – BonsaiOak
    Commented Apr 21 at 4:31

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