By Doug Jones, MMBR
Midwest Devices LLC
http://www.midwestdevices.com
1-816-204-1357
RC Time Constant Formulas
1 Time Constant in seconds = R*C. t = RC
Capacitors are considered charged after 5 equal time constants.
C = t / R (for 1 time constant)
“t” is Measured at 63.2% of Vs
SPDT Switch S1
Definitions:
t = Elapsed charging time in seconds
RC = Time Constant
R = Series resistance in Ohms
C = Series capacitance in Farads
Vs = Constant DC battery voltage in Volts
Vc = Instantaneous DC voltage across C in Volts
x = Time constant number/multiplier
Time Ratio = t/RC
S1 (a) NO
Charge
VC
C
VS
Discharge
S1 (b)
NC
R
Use these equations. x=time constant number i.e 0.5, 1, 2, 3, 4, 5
Vc / Vs = (1- e-x)
VC = VS(1- e-x )
Or from the Universal Time Constant Chart:
After 1 Time Constant Vc = 0.632(Vs)
After 2 Time Constants Vc = 0.865(Vs)
And so on through 5 time constants or fractions thereof.
VR
Find value of the capacitor:
We know battery voltage “Vs” and the
value of “R”. By measuring the time to charge
Vc to one time constant which is 63.2% of Vs
we find “t”. Calculate capacitance using C = t / R.
UNIVERSAL Time Constant Chart
Δ% / Δt - Graph of “Time Constants” vs “%”
% of Maximum Voltage = 100(1-e-x(t/RC) )
Charge Time
The VALUE of “t/RC” does not matter!
Assign a convienient value of “1” to “t/RC”
% of Maximum Voltage
100
If t/RC = 1 Then:
% of Max Voltage = 100(1-e-x )
t / xRC
% Max V
x=0.5
39.3%
x=1.0
63.2%
x=1.5
77.7%
x=2.0
86.5%
x=2.5
91.8%
x=3.0
95.0%
x=3.5
97.0%
x=4.0
98.2%
x=4.5
98.9%
x=5.0
99.3%
90
80
70
% Discharge = 100% - %Chg
t = 63.2% of Vs
60
50
40
30
20
10
0
Chart of Time RATIO vs “%” intersect points @1/2RC
intervals up to 5RC. Notice the graph has more RED DOT
intersects than computed above. I needed the extra
intersects to draw an accurate charging curve.
Discharge
0.5RC
1RC
1.5RC
2RC
3RC
4RC
5RC Time in Time Constants
UNIVERSAL Time Constant Chart
% = 100(1-e-x(t/RC)) = 100(1-e -x(Time RATIO))
t /RC is simply a time RATIO. This time RATIO determines the intercepts - not the specific VALUES of t or RC!
If t = RC then the ratio t/RC = 1:1 = one time constant = 1RC.
(RC = Time Constant, x = multiplier)
If t = 0.5RC then the ratio = 0.5:1 = 1/2 time constant = 0.5RC
Copyright© 2010-2015 Midwest Devices LLC, Doug Jones