RC Times

How long does it take a capacitor of 100 nF to charge up to 3 Volts when it is connected to a 12V supply voltage through a 47 kΩ resistor? Or what capacitor value do I need if I want to charge it to 6 V in 33 ms when connected to a 9 V supply through a 15 kΩ resistor?
And I can think of quite some other questions like these for any given RC circuit. This program will help you answer these questions, no matter which one of the 5 parameters is unknown.

Formulas

Ub = Uc / ( 1 - e🠕 ( -t / (R • C) ) )

Uc = Ub . ( 1 - e🠕 ( -t / (R • C) ) )

R = t / ( C • -LN( ( Ub - Uc ) / Ub ) )

C = t / ( R • -LN( ( Ub - Uc ) / Ub ) )

t = R • C • -LN ( ( Ub - Uc ) / Ub )

Where:
Ub is the net driving voltage. If the capacitor is at 0V this will simply be the supply voltage. If not, subtract the starting voltage across the capacitor from the supply voltage to get Ub.
Uc is the voltage across the capacitor after t seconds.
R is value of the series resistor of the capacitor.
C is the value of the capacitor itself.
t is the time it takes the given capacitor to charge up to the voltage Uc.

The Program

	000–
h LBL A	001–	25 13 11
STO 1	002–	23 1	Store Ub
R/S	003–	74
STO 2	004–	23 2	Store Uc
R/S	005–	74
STO 3	006–	23 3	Store R
R/S	007–	74
STO 4	008–	23 4	Store C
R/S	009–	74
STO 5	010–	23 5	Store t
g X=0	011–	15 71
GTO 5	012–	22 5	T is the unknown
RCL 4	013–	24 4
g X=0	014–	15 71
GTO 4	015–	22 4	C is the unknwon
RCL 3	016–	24 3
g X=0	017–	15 71
GTO 3	018–	22 3	R is the unknwon
RCL 2	019–	24 2
g X=0	020–	15 71
GTO 2	021–	22 2	Uc is the unkown
RCL 1	022–	24 1
g X=0	023–	15 71
GTO 1	024–	22 1	Ub is the unknown
CLX	025–	34	All values are known,
h RTN	026–	25 12	there's nothing to calculate!
h LBL 1	027–	25 13 1	Calculate Ub
RCL 5	028–	24 5
RCL 3	029–	24 3
÷	030–	71
RCL 4	031–	24 4
÷	032–	71
CHS	033–	32
g EX	034–	15 1
1	035–	1
X⇋Y	036–	21
–	037–	41
RCL 2	038–	24 2
X⇋Y	039–	21
÷	040–	71
h RTN	041–	25 12
h LBL 2	042–	25 13 2
RCL 5	043–	24 5
RCL 3	044–	24 3
÷	045–	71
RCL 4	046–	24 4
÷	047–	71
CHS	048–	32
g EX	049–	15 1
1	050–	1
X⇋Y	051–	21
–	052–	41
RCL 1	053–	24 1
×	054–	61
h RTN	055–	25 12
h LBL 3	056–	25 13 3
RCL 4	057–	24 4
GTO 0	058–	22 0
h LBL 4	059–	25 13 4
RCL 3	060–	24 3
h LBL 0	061–	25 13 0
RCL 1	062–	24 1
RCL 2	063–	24 2
–	064–	41
RCL 1	065–	24 1
÷	066–	71
f LN	067–	14 1
CHS	068–	32
×	069–	61
RCL 5	070–	24 5
X⇋Y	071–	21
÷	072–	71
h RTN	073–	25 12
h LBL 5	074–	25 13 5
RCL 1	075–	24 1
RCL 2	076–	24 2
–	077–	41
RCL 1	078–	24 1
÷	079–	71
f LN	080–	14 1
CHS	081–	32
RCL 3	082–	24 3
×	083–	61
RCL 4	084–	24 4
×	085–	61
h RTN	086–	25 12

Operation

For this program we need 4 known parameters and we want the calculator to come up with the 5th parameter, no matter which one it is. That doesn't fit on the stack any more, so we're going to use the memory locations 1 to 5 to store all the parameters.
After entering the first parameter you start the program by pressing the A key. This stores the first parameter in memory location 1. All subsequent parameters are simply entered when you press the R/S key, storing each value in the subsequent memory locations up to 5.
You should make the unknown parameter 0, which indicates that you want to know that value. Feel free to fool the calculator by entering multiple parameters with the value of 0, but don't blame the calculator when it comes up with a rubbish answer or even an error. In case you have not entered a parameter with the value 0 at all, the calculator returns the value 0.

The parameters are to be entered in the order: Ub, Uc, R, C and t.

Examples

As our first example we'll try to find out how long it takes to charge a capacitor of 10 nF from 2V to 4V. The capacitor is placed in series with a 10 kΩ resistor with a total supply voltage of 9V.
This means that Ub is 9V minus the starting voltage of 2V, the rest can be entered as is.

7A 4R/S 10EEX3R/S 10EEX9CHS 0R/S and the answer will be 84.73 µs.

In an other example I want to know to what voltage a capacitor of 220 nF is charged when it is connected in series with a resistor of 47 kΩ across a voltage of 12V. What will be the voltage after 10 ms?

12A 0R/S 47EEX3R/S 220EEX9CHS 10EEX3CHSR/S and the answer will be 7.438V.