| Electronics > Beginners |
| Four questions about (Super) capacitors in series |
| << < (6/6) |
| havewattwilltravel:
Because using those does not enable me to understand what's going on! Clearly, we're failing to communicate (ironically illustrating my point). Thank you for your help. |
| Brumby:
People learn differently, so further discussion on this is a pointless tangent. Let's not continue down that path any more. Please. |
| Brumby:
Without regurgitating much the same in my own words, this gets my vote as a good answer... --- Quote from: helius on August 23, 2018, 07:24:35 pm --- --- Quote from: havewattwilltravel on August 23, 2018, 06:26:56 pm ---1. Suppose I were to put 10 perfectly matched 1F capacitors in series and charge the series to 10V. Would each capacitor actually have the same charge/voltage, or would they vary slightly (and consistently) by position, with the outermost capacitors charged slightly more than the inner ones? --- End quote --- The charge on each capacitor in series is the same because charge is conserved. The total charge put onto one plate of a capacitor is equal to the charge out of the other plate, and this is transitive across all of the series capacitors. The voltage on each capacitor will be according to V = C/Q; so if they all have the same capacitance, they will all have the same voltage. --- Quote ---(I'm thinking even if the ESR were the same for each cap, there's still a time delay as they charge that would leave them imbalanced.) --- End quote --- ESR doesn't matter here, and there is no time delay. Each capacitor is charged simultaneously—obviously not in a bare instant, but the current through the series string charges them at the same rate. --- Quote ---2. Suppose I charged each capacitor to exactly 1V and left them for 10 days. If the leakage current was the same for each cap, would the charge/voltage be the same, or would they again vary (consistently) by position? (Would some of the leakage current effectively charge the outer caps rather than just heating them all evenly?) --- End quote --- Leakage is modeled by a parallel resistance, not a current; but you specified that the leakage currents were equal. Well, okay: if you integrate a current over a period of time, the result is a certain change in charge. This has nothing to do with capacitors. --- Quote ---3. If that same string were partially discharged, would the resultant voltage on the outer capacitors be slightly less than those on the inner capacitors? (Because of ESR, wouldn't the outer caps be discharging into slightly lower resistance than the inner ones?) --- End quote --- By the same reasons as (1), they discharge equally. ESR is a series resistance, and several resistors in series are equivalent to one. Different ESR does not effect them differently, they all see the same series resistance. --- Quote ---4. Assume I were to use real capacitors and compensate for the individual differences in capacitance and leakage by putting additional capacitors and resistors in parallel with each capacitor in the string to make them equal. Would they remain balanced over time, or do the parameters for each capacitor vary individually so much over time that they'd always get out of balance? --- End quote --- You didn't specify what "make them equal" means. As noted above, variations in capacitance and ESR have no effect whatsoever on the state of charge; the voltage will depend on the capacitance of each one according to the capacitor equation. The only reason to balance capacitors in series is leakage, since it acts as a parallel resistor that discharges each cap separately. If the caps have different leakage, some will discharge more than others—this can cause problems when the series is charged again, and the caps with lower leakage start from a higher state of charge, which could make them exceed their voltage specification. The way to deal with this is to place a high-value resistor in parallel with each individual capacitor, in effect overwhelming the unknown leakage with a predictable discharge. --- End quote --- |
| helius:
--- Quote from: JS on August 24, 2018, 04:14:18 am ---I would mention something that's not exactly on topic but I think it should be mentioned here... --- End quote --- I considered mentioning those practical aspects, but from the way the question was phrased I guessed it was just a theoretical problem. Series capacitors are rarely used unless the working voltage of the available components is too low for the application. So a long series string of capacitors usually means very high voltages, as in a Marx Bank. The other case is when working voltages are super low, like the 2.7V of EDLCs/ultracaps. In either case, attention must be paid to the effects of different leakages making the caps unbalanced, because the caps are already being charged to their working voltage limit (or you wouldn't need a series string of them). |
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