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Illustration Voltage-Time Graph of Resistor - Charging a Capacitor

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.