Physics

The key is recognizing that charge in an RC circuit grows exponentially, not linearly. At time $t = \tau$ (one time constant), the charge follows $Q(t) = Q_f(1 - e^{-t/\tau})$, where $Q_f$ is the final charge. Plug in $t = \tau$ and you'll see the exponential decay factor becomes $e^{-1}$ — a specific, memorable number that tells you exactly what fraction of the final charge has built up.

The key is recognizing that charge in an RC circuit grows exponentially, not linearly. At time $t = \tau$ (one time constant), the charge follows $Q(t) = Q_f(1 - e^{-t/\tau})$, where $Q_f$ is the final charge. Plug in $t = \tau$ and you'll see the exponential decay factor becomes $e^{-1}$ — a specific, memorable number that tells you exactly what fraction of the final charge has built up.