Calculator · Electrical Engineering
RC Charge & Discharge Calculator
A capacitor C starting at V0 is connected at t = 0 through R to an ideal source Vf. Its voltage moves exponentially from V0 toward Vf with time constant τ = R·C — charging, discharging, or any other step.
Inputs
Vf = 0 is a discharge through R. The current is the capacitor current, positive when it charges the capacitor toward a more positive voltage.
Results
Time constant τ = R·C
100 ms
Capacitor voltage Vc(t)
3.161 V
Transition completed
63.21 %
| Behaviour | Charging (|Vc| rising) |
|---|---|
| Current i(t) | 1.839 mA |
| Charge Q(t) = C·Vc | 316.1 µC |
| Stored energy E(t) = ½·C·Vc² | 499.5 µJ |
Assumptions
- · ideal DC source Vf in series with R and an ideal capacitor
- · Vc(0) = V0; the source is applied at t = 0
- · i is the capacitor current (passive sign: positive charges the capacitor)
Explore in the Lab
Open this transient in the Capacitors & Transients Lab
Same R, C, V0, Vf; the selected time is t.
Technical reference
τ = R·C
Vc(t) = Vf + (V0 − Vf)·e^(−t/τ)
i(t) = C·dVc/dt = ((Vf − V0)/R)·e^(−t/τ)
Q(t) = C·Vc(t), E(t) = ½·C·Vc(t)²
- R
- series resistance (> 0)[Ω]
- C
- capacitance (> 0)[F]
- V0
- capacitor voltage at t = 0[V]
- Vf
- source voltage = final capacitor voltage[V]
- t
- time since the step (≥ 0)[s]
After 1τ the transition is 63.2 % complete; after 5τ, 99.3 %.
Ideal components: no leakage, no source resistance beyond R.