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Time domain math - learning by doing last semester first

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Hi forum, fellow members.

I was lurking around on the net (in another forum I had to admit, please don't arrest me) and found a question about how to solve a capacitor charging when there was both a resistor and voltage follower in the mix. So using superposition or the theorem to make everything into current or voltage source would be on my short list to solve that particular problem. But then there was one clever dude suggesting using time domain math to solve the problem (that is voltage as function of time).

Back to school - this is the actual problem
I obviously didn't post this thread to work out a basic RC circuit charging problem - I like to think of this post more like an myself-introduction kind of subject - that's why I choosed members lounge.
This story is from eleven years ago back in time, so I wouldn't remember much anyway since I don't have a job that I need to do this kind of math solving. The subject at scool spanned over two semesters.

Semester one: We had this very extreme smart teacher (Supa dupa IQ+++) and he started right away solving math equations. All the methods and rules was hammered into our student heads. But he forgot something very important - he acually spend one whole semester hammering on those rules and formulas but never ever was able to use any of this for electrical problem solving. Never - it was math only (I'm confident that the teacher has never dealt with anything involving electric circuits). Got very boring, and after all what purpose did this math anyway, I asked myself.

Semester two: Change of teacher. This one have teached electrical circuits hes whole career and was very able to explaining all the practical use for the math. That time - I understood that this was something that may come handy. But realized we started totally backwards, because by now we had only doing math solving without being demonstrated any practical use for the material.

Obviously I beleived the teacher for second semester was the greater one because he was able to use the time domain math to solve real solutions.
But - because of the swap of semesters in order of teaching methods, I feel I never got the real understanding of the material. Example - If I was told today to solve a very simple question of charging a RC circuit using time domain - I'm simply not capable to do that, I don't know where to start.

Say I want to spend some hours at home to refresh - where to go to start? I haven't got any book when at first semester, the teacher always used notes created on Powerpoint so they are to no use today.

[edit / ot]
Maybe it's time to do something to the avatar now, have had that weird resistor for a while. This new gui is a little to big to fit the size of an avatar.
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Lost a bit on the Time domain concepts that I can recall. Time based on known current flow such as a resistor with the capacitors value not fully relevant as the resistor plays the key role in the capacitors charge / discharge rate.

The Wiki info on RC circuit tends to leave me behind. Formulations.

Tho, I'm getting that this is all ready known in the part of resistance results altering capacitor rate, just not so much the math form that results the statements that would show the voltage flow. Voltage being a product of current.

Also the capacitors ESR added to the resistance value results the more close to ideal time. Or determining the capacitors ESR by means of a possible known R/C time value via the source voltage being known and the resistors absolute value at temperature known, the difference in the capacitors charge/discharge rate, fast/slow against the known (what it should be time) could indicate by that percent a means to determine the ESR of a capacitor being high or low. Also if a measurement means that would not interfere with the test by sapping power away unless the measuring devices known requirement was appended to the test. Op amp requires this much input current and so an depending on what characteristics of the device are if one were to be used. This current pull would derate the test time by the percent of continuous pull of the test device used, if any. A very high impedance scope would yield losses of the test leads greater than the scope.

I'm trying to jostle memory of this by using what parts got me to an partial understanding, and not doing so very well.
should I say welcome to the club? Btw one very often used tem in my language may translate to something similar to "that information is written down in the great book of lost memories".

The image can be stretched or shrinked almost unlimited, as it is based on a cad drawing. Also the program I use (Inkscape) have the ability to resize figures overall size but retain the thickness of the lines.

As the figure get smaller - even if line thickness is the same - it get harder to see that it is supposed to resemble windings symbol.
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