Capacitor charging

If you are using capacitors (like X2) in your design, and you want to control the charging of the capacitor with a resistor or just to calculate the charge time, here is a way to do that.

The following formulas describe the Voltage over the capacitor (Vc) and the current through it (Ic).

$$Vc=Etimes (1-e^{-frac{t}{tau }})$$

$$Ic=frac{E}{R}times e^{-frac{t}{tau}}$$

Vc: Capacitor voltage.
E:   Charging voltage.
Ic:  Capacitor current.
R:   Resistor.
τ:   Tau is the time constant τ = R x C in seconds.
t:    time in seconds from V to Vc.

A = Charging curve for the capacitor and B = discharging curve for the capaciter.

By rewriting the formulas we get:

$$t=-ln (1-frac{Vc}{E})times Rtimes C$$

$$R = frac{t}{-ln (1-frac{Vc}{E})times C}$$

You can rewrite it to fit your specific purpose.

Here is a example of calculating the charging resistor for charging capacitor.

Let us say C = 1uF, E = 10Vdc and Vc = 7,5Vdc (the level we want to reach). We want to reach Vc in 0,1s.

Now what is the value of the resistor R by using the formula above:

$$R=frac{t}{-ln (1-frac{Vc}{E})times C}=frac{0,1}{-ln (1-frac{7,5}{10})times 1uF}=72Kohm$$

Remember to check for Power in the resistor. No problem in this case.