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Provide any two of \( R \), \( C \), \( \tau \) — the third is solved. Optionally provide a time \( t \) and an initial or supply voltage to calculate the charging or discharging voltage at that time.
The RC time constant \( \tau \) characterises how quickly a capacitor charges or discharges through a resistor: \[ \tau = R \cdot C \] Where \( R \) is in Ohms and \( C \) is in Farads, giving \( \tau \) in seconds. It is the single most important parameter of any RC circuit — it sets the speed of every transition.
When a discharged capacitor is connected to a supply voltage \( V_s \) through a resistor, the voltage across the capacitor rises exponentially: \[ V(t) = V_s \cdot \left(1 - e^{-t/\tau}\right) \] After one time constant the capacitor has charged to \( 1 - 1/e \approx 63.2\% \) of \( V_s \). After five time constants it is considered fully charged: \[ \begin{align} t = 1\tau &\Rightarrow V = 63.2\%\ V_s \\ t = 2\tau &\Rightarrow V = 86.5\%\ V_s \\ t = 3\tau &\Rightarrow V = 95.0\%\ V_s \\ t = 4\tau &\Rightarrow V = 98.2\%\ V_s \\ t = 5\tau &\Rightarrow V = 99.3\%\ V_s \end{align} \]
When a fully charged capacitor discharges through a resistor, the voltage decays exponentially: \[ V(t) = V_0 \cdot e^{-t/\tau} \] After one time constant the voltage has dropped to \( 1/e \approx 36.8\% \) of \( V_0 \). The decay is the mirror image of the charging curve.
Given any two of \( R \), \( C \), \( \tau \), the calculator solves for the third:
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