Capacitor Charging Time calculator, Formula, Calculation

Capacitor Charging Time calculator:

Enter the series resistance and the capacitor then press the calculate button to get the RC time constant. Change the value inside the field.

Capacitance: μF
Resistance: Ohms
Time Constant: Sec

Capacitor Charging Time Formula:

In the RC series circuit, the Capacitor time constant τ(s) in seconds is equal to the 0.000001 of capacitance C (μF) in microfarad times of the series resistance R (Ω) in Ohms. Hence the time constant formula can be written as,

 τ (s) = 0.000001 x R (Ω) x C (μF)

Time constant = 0.000001 x resistance x capacitance.

In the above obtained time constant, the capacitor charges 63% for one time constant. To get full charge the capacitor up to 100% means, it takes 5 times of the time constant.

capacitor time constant
capacitor time constant

Let us elaborate.

The voltage Vc in volts across the capacitor is equal to the Supply input voltage Vs in volts times of the one minus e-τ/RC. Hence the formula will be,

Vc = Vs (1 – e-τ/RC)

Here to get a full charge, the voltage across the capacitor and the input supply should be the same.

The formula,

Vc = Vs (1 – (1/eτ/RC))

Look at the formula, when increasing the resistance and the capacitance increases the capacitor charging time.

For one times of

τ (s) = 1 x R (Ω) x C (μF)

Vc = Vs (1- 1/e1) = Vs (1-1/ 2.718) = 1 – 0.367918 = 63.2%

For two times of time constant,

Vc = Vs (1- 1/e2) = Vs (1-1/ 7.389) = 86.2%

For Three times of time constant,

Vc = Vs (1- 1/e3) = Vs (1-1/ 20.086) = 95.3 %

For Four times of time constant,

Vc = Vs (1- 1/e4) = Vs (1-1/ 54.598) = 98.1 %

For Five times of time constant,

Vc = Vs (1- 1/e5) = Vs (1-1/ 148.413) = 99.3 %

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