Equation to figure out the resistance to charge capacitors evenly

Depends on what you mean by 'to charge evenly'. Any network of capacitors (whether in series, parallel, or a hybrid of both) can be reduced to a single equivalent capacitance that will charge evenly. Capacitors in parallel will always be charged to the same voltage. Capacitors in series will always each acquire the same electric charge (in coulombs) but the voltage across any capacitor will be in accordance with the equation farads=coulombs/volt.

 

The given reference speaks of leakage resistance on the order of 100 million megohms. Capacitor leakage/soakage is normally a concern in sample & hold applications using plastic film capacitors. Even so, leakage is not a concern during the charge cycle. If electrolytic capacitor leakage is a concern in your application, then perform a measurement of the leakage resistance and include that resistance with the capacitance in your circuit model for analysis. Please post your circuit model.

 

Bob Pease uninformed?

Edit:

In response to the original question. The problem of uneven charging of multiple capacitors only happens if they are connected in series. It is often solved by connecting a resistor across each capacitor (resistor values are the same if capacitor values are the same, which is common). This is equivalent to connecting a single resistor, with a value equal to the sum of the resistors, in parallel with the combined capacitor, and it will cause the capacitor to discharge following the usual logarithmic curve. In some cases this is not important - for example if you're balancing the voltage across two capacitors that are used in a smoothing or decoupling application, where the charge is being continuously topped up. In other cases it will be significant - a sample-and-hold circuit is an obvious example.

An alternative for fixed DC voltage applications such as smoothing or decoupling capacitors is to use zener diodes with small series resistors. This will also ensure that individual capacitors are not exposed to overvoltage even briefly.

If you tell us what you actually want to do, we will be able to give you more applicable advice.

 

lol, I suspect we are headed toward a "capacitor energy storage system " with zero losses...."obviously" a more energy efficient storage system than super conductors It is truly a shame that those physicist working on super conductors never thought of using capacitors for storage,

But maybe there is a different reason for needing 11 capacitors series connected across a 12Vdc potential or 9 Capacitors connected in Series/Parallel across a 5Vdc source? It is hard to say....

To the OP:
For a discussion about the inefficiency of capacitor stored energy: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capeng2.html#c4

Regardless of what you believe, capacitors are not an efficient means of storing energy nor shifting voltage levels. Since I cannot fathom any other reason for connecting series/parallel combinations of capacitors to a DC source, I must conclude that you were working under the assumption that a capacitor is the "perfect energy storage device"; let me assure you, this is NOT fact.

Fish

 

Yes, I assume it was just a simplification and approximation to put the discharge into context with his other calculations.