Formula Charging Process of a Capacitor (RC Circuit) Voltage at Resistor Source voltage Capacitance Electrical Resistance Time
$$U_{\text R}(t) ~=~ U_0 \, \mathrm{e}^{-\frac{t}{R\,C}}$$ $$U_{\text R}(t) ~=~ U_0 \, \mathrm{e}^{-\frac{t}{R\,C}}$$ $$U_0 ~=~ U_{\text R}(t) \, \mathrm{e}^{\frac{t}{R\,C}}$$ $$C ~=~ - \frac{ t }{ \ln\left( \frac{ U_{\text R}(t) }{U_0} \right) \, R }$$ $$R ~=~ - \frac{ t }{ \ln\left( \frac{ U_{\text R}(t) }{U_0} \right) \, C }$$ $$t ~=~ - \ln\left( \frac{ U_{\text R}(t) }{U_0} \right) \, R \, C$$
Voltage at Resistor
$$ U_{\text R}(t) $$ Unit $$ \mathrm{V} $$ Voltage measured between the two ends of the resistor. The voltage at the series resistor decreases exponentially with time during charging.
Source voltage
$$ U_0 $$ Unit $$ \mathrm{V} $$ Constant voltage applied to the RC circuit for charging. This is the voltage at time \(t = 0 \).
Capacitance
$$ C $$ Unit $$ \mathrm{F} $$ Capacitance is a characteristic quantity of the capacitor and tells how many charges must be brought onto the capacitor to charge the capacitor to the voltage \( 1 \, \mathrm{V} \).
Electrical Resistance
$$ \class{brown}{R} $$ Unit $$ \mathrm{\Omega} $$ Resistor connected in series with the capacitor. The resistance, together with the capacitance, has an influence on how fast the capacitor can charge.
Time
$$ t $$ Unit $$ \mathrm{s} $$ At the time \( t = 0\) a voltage \( U_{\text R}(0) = U_0\) was present at the resistor of the RC element. With time, \(U_{\text R}(t)\) decreases exponentially to zero.