Capacitor Charging & Discharging Simulator
Visualize RC circuit transients — voltage, current and time constant τ in real time
Controls
Circuit Parameters
1.0 kΩ
100 μF
12.0 V
0.0 V
Results
Time constant τ = RC
—
63.2% reached
—
99% reached
—
Peak current I₀
—
Stored energy E = ½CV²
—
Voltage v(t)
Current i(t)
Theory
The time constant of a series RC circuit:
$\tau = RC$
Charging (switch closed, initial voltage $V_\text{init}$):
$v(t) = V_0 + (V_{\text{init}} - V_0)\,e^{-t/\tau}$
$i(t) = \dfrac{V_0 - V_{\text{init}}}{R}\,e^{-t/\tau}$
$i(t) = \dfrac{V_0 - V_{\text{init}}}{R}\,e^{-t/\tau}$
Discharging (switch open, initial voltage $V_0$):
$v(t) = V_0\,e^{-t/\tau}$
$i(t) = -\dfrac{V_0}{R}\,e^{-t/\tau}$
$i(t) = -\dfrac{V_0}{R}\,e^{-t/\tau}$
Energy stored in the capacitor:
$E = \dfrac{1}{2}CV^2$
At $t = \tau$, the capacitor voltage reaches $(1 - e^{-1}) \approx 63.2\%$ of the final value. At $t = 5\tau$ it is 99.3% complete.