Calculation Formula of capacitor charge discharge time

Calculation Formula of capacitor charge discharge time

 

 

Set, V0 as the initial voltage value on the capacitor;
V1 is the final charged or placed voltage value of the capacitor;
VT is the voltage value of the capacitor at t time.
Then,
Vt = "V0" + (V1-V0) * [1-exp (-T/RC)]
Or,
T = rc * ln [(V1-V0)/(V1-Vt)]

For example, a battery with a voltage of E is charged to a capacitor C with a initial value of 0 through R.
V0 = 0, V1 = E, so the voltage charged to the T moment capacitor is:
Vt = "E" * [1-exp (-T/RC)]

For another example, capacitor C with initial voltage e is discharged through R.
V0 = E, V1 = 0, so the voltage put on the T-moment capacitor is:
Vt = "E" * exp (-T/RC)

Another example is that capacitor C with initial values of 1/3 VCC is charged by R, and the final value of charge is
VCC: How long does it take to charge 2/3 VCC?
V0 = VCC/3, V1 = VCC, VT = 2 * VCC/3, so
T = "RC" * ln [(1-1/3)/(1-2/3)] = rc * ln2
= 0.693rc

Note: The above exp () indicates the base-e exponent function; Ln () indicates the base-e logarithm function.
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