Formula: Discharging Capacitor Voltage Anfangsspannung Capacitance Electrical Resistance Time
$$U_{\text C}(t) ~=~ U_0 \, \mathrm{e}^{-\frac{t}{R\,C} }$$
$$U_{\text C}(t) ~=~ U_0 \, \mathrm{e}^{-\frac{t}{R\,C} }$$
$$U_0 ~=~ U_{\text C}(t) \, \mathrm{e}^{\frac{t}{R\,C} }$$
$$C ~=~ - \frac{t}{ \ln\left( \frac{U_{\text C}(t)}{U_0} \right) \, R }$$
$$R ~=~ - \frac{t}{ \ln\left( \frac{U_{\text C}(t)}{U_0} \right) \, C }$$
$$t ~=~ - \ln\left( \frac{U_{\text C}(t)}{U_0} \right) \, R \, C$$
Voltage
$$ U_{\text C}(t) $$ Unit $$ \mathrm{V} $$
This is the voltage measured across the capacitor (e.g. between the two capacitor plates). When the capacitor is discharged, the voltage decreases exponentially with time \(t\). At the end of the discharge process, it reaches approximately zero.
Anfangsspannung
$$ U_0 $$ Unit $$ \mathrm{V} $$
Elektrische Spannung auf dem Kondensator vor dem Entladen. Also die Spannung zum Zeitpunkt \( t = 0\).
Capacitance
$$ C $$ Unit $$ \mathrm{F} $$
Electrical 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 \( 1 \, \text{V} \). Together with the resistance \(R\), the capacitance determines how fast the capacitor discharges.
Electrical Resistance
$$ \class{brown}{R} $$ Unit $$ \mathrm{\Omega} $$
Resistor with the resistance \( R \) connected in series with the capacitor. The Resistance has an influence on how fast the capacitor can discharge.
Time
$$ t $$ Unit $$ \mathrm{s} $$
The capacitor, with the source voltage \( U_0 \), is now discharged by short-circuiting the capacitor. The discharge process happens with a time delay (exponential decay of \( U_{\text C}(t) \)).