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Fill in the known variables. Leave exactly one of \( t \) or \( V(t) \) empty — the calculator solves for it. Provide \( R \) and/or \( \tau \) for RC exponential discharge, or \( I \) for constant current discharge.
This calculator covers two physically distinct discharge scenarios: exponential RC discharge and constant current discharge.
When a charged capacitor discharges through a resistor, the voltage, current, and charge all decay exponentially: \[ V(t) = V_0 \cdot e^{-t/\tau} \] \[ I(t) = \frac{V_0}{R} \cdot e^{-t/\tau} \] \[ Q(t) = C \cdot V_0 \cdot e^{-t/\tau} \] where \( \tau = R \cdot C \) is the time constant. All three quantities share the same exponential envelope — only the scaling factor differs.
To find the time at which the voltage reaches a target value \( V(t) \), rearrange: \[ t = -\tau \cdot \ln\!\left(\frac{V(t)}{V_0}\right) \]
\( \tau = R \cdot C \) sets the speed of the discharge. After one time constant the voltage has dropped to \( 1/e \approx 36.8\% \) of \( V_0 \). After five time constants the capacitor is considered fully discharged for most practical purposes: \[ \begin{align} t = 1\tau &\Rightarrow V = 36.8\%\ V_0 \\ t = 2\tau &\Rightarrow V = 13.5\%\ V_0 \\ t = 3\tau &\Rightarrow V = 5.0\%\ V_0 \\ t = 4\tau &\Rightarrow V = 1.8\%\ V_0 \\ t = 5\tau &\Rightarrow V = 0.7\%\ V_0 \end{align} \]
When a capacitor is discharged by a constant current source — such as a current-regulated load or a charge pump — the voltage decreases linearly rather than exponentially: \[ V(t) = V_0 - \frac{I \cdot t}{C} \] Rearranged to solve for the time to reach a target voltage: \[ t = \frac{C \cdot (V_0 - V(t))}{I} \] The capacitor fully discharges at \( t_{\text{max}} = C \cdot V_0 / I \).
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