REAL-TIME DATA
Capacitor Volts ($V_C$)0.00 V
Current ($I$)0.00 A
Time Const ($\tau=RC$)1.0 s
CHARGE (Connect Battery)
DISCHARGE (Short)
■ Time Constant $\tau = RC$:
Defines the speed of transient decay. After $1\tau$, the system reaches $\approx 63\%$ of its final state. By $5\tau$, it is essentially at steady state ($>99\%$).
■ Charging Phase:
$V_C(t) = \varepsilon (1 - e^{-t/\tau})$
$I(t) = \frac{\varepsilon}{R} e^{-t/\tau}$
■ Discharging Phase:
$V_C(t) = V_0 e^{-t/\tau}$
$I(t) = -\frac{V_0}{R} e^{-t/\tau}$
Defines the speed of transient decay. After $1\tau$, the system reaches $\approx 63\%$ of its final state. By $5\tau$, it is essentially at steady state ($>99\%$).
■ Charging Phase:
$V_C(t) = \varepsilon (1 - e^{-t/\tau})$
$I(t) = \frac{\varepsilon}{R} e^{-t/\tau}$
■ Discharging Phase:
$V_C(t) = V_0 e^{-t/\tau}$
$I(t) = -\frac{V_0}{R} e^{-t/\tau}$