Illustration Voltage-Time Graph of Resistor - Charging a Capacitor

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When charging the capacitor with capacitance $$C$$ via a series resistor $$R$$, the voltage at the series resistor has an exponential behaviour. The voltage $$U_{\text R}(t)$$ at the resistor decreases exponentially with time $$t$$:$$U_{\text R}(t) = U_0 \, \mathrm{e}^{-\frac{t}{R\,C}}$$

When $$t$$ goes to infinity, the voltage $$U_{\text R}(t)$$ goes to zero.