Capacitor calculator

Capacitors behave backwards from resistors, and the reason is geometric, not arbitrary. Resistance opposes current, so an extra path reduces it. Capacitance stores charge on plates, so extra plate area increases it: parallel capacitors are effectively one capacitor with larger plates and the values add. Series stacks the separation between the plates instead, which lowers capacitance, so the reciprocal sum applies and the total falls below the smallest member.

Voltage rating cuts the other way

In parallel there is no trade at all: every capacitor sees the full supply voltage, so the lowest rating in the set is the limit for the whole bank. Series is how you get a rating higher than any single part offers, and it comes with a trap. The voltage only divides evenly if the parts are matched and their leakage currents are similar. In practice leakage differs, the string drifts, and one capacitor ends up carrying more than its share until it fails, which then puts the full voltage across the next one. Any series string handling real voltage needs balancing resistors across each capacitor to hold the division steady, which is why you see them on every high-voltage bank.

Paralleling buys two things beyond capacitance. Equivalent series resistance falls roughly as the reciprocal of the count, which is why a bulk bank is built from several smaller parts instead of one large one. And a small ceramic sitting beside a big electrolytic is not there for its capacitance at all; it has far lower inductance and handles the fast transients the electrolytic cannot follow.

Charging is exponential, so nothing is ever full

One time constant is R times C and reaches 63.2%. Five leaves under 1% remaining, which is smaller than component tolerance, and that is why the figure quoted here is five tau and never a time to "fully charged". The shape matters as much as the number: charging is fastest at the start and slows continuously, so the last few per cent take as long as the first sixty.

Nothing limits the initial current except the series resistance, because an empty capacitor behaves like a dead short at the instant of switch-on. On a large supply that is what welds relay contacts and blows fuses. An inrush limiter is a resistor placed in series to hold the first surge down, shorted out by a relay once the capacitor is mostly charged. The same arithmetic run backwards tells you how long a board takes to become safe to touch, and the honest advice there is to confirm discharge with a meter instead of trusting a calculation.

The inductor is the mirror again

A capacitor opposes changes in voltage and passes high frequencies. An inductor opposes changes in current and blocks them, so its reactance rises with frequency where capacitive reactance falls. That makes it a good series filter against switching noise at hundreds of kilohertz and a poor one against 50 or 60 Hz mains hum, where the reactance is simply too small to do anything. At the frequency where the two reactances cancel you have resonance, which is the whole basis of an LC filter or a tuned circuit.

The stored-energy figure is the one that bites in switching supplies. Interrupting an inductor carrying current forces that energy to go somewhere, and with no flyback path it appears as a voltage spike large enough to destroy whatever did the switching.