RC Circuit Time Constant — Theory
A series RC circuit responds exponentially to a voltage step. The characteristic time scale is the
time constant:
\( \tau = RC \).
After one time constant, the capacitor voltage has moved about 63% of the way from its initial value toward its final value.
1) Time constant
2) General step response
For a Thevenin step to a constant final voltage \(V_\infty\) with capacitor initial voltage \(V_0\), the capacitor voltage is
3) Charging and discharging special cases
4) Charge and current
Charge on the capacitor is proportional to its voltage, and the current follows from the resistor drop:
5) The 63% fact at \(t=\tau\)
The exponential gives a simple landmark: \(e^{-1}\approx 0.3679\).
For a 0→\(V_\infty\) step, at \(t=\tau\):
6) Plot interaction note
The plot shows \(V_C(t)\), \(I(t)\), or \(Q(t)\) from \(t=0\) to the chosen \(t_{\max}\).
The “cursor fraction” slider only moves a dot along the plotted time range; it does not change your input \(t\).
