Formula: Capacitor - Discharge Process (RC Circuit) Discharge current Capacitance Electrical Resistance Time
$$I(t) ~=~ -I_0 \, \mathrm{e}^{-\frac{t}{R\,C}}$$
$$I(t) ~=~ -I_0 \, \mathrm{e}^{-\frac{t}{R\,C}}$$
$$I_0 ~=~ -I(t) \, \mathrm{e}^{\frac{t}{R\,C}}$$
$$C ~=~ \frac{ t }{ \ln\left( \frac{I(t)}{I_0} \right) \, R }$$
$$R ~=~ \frac{ t }{ \ln\left( \frac{I(t)}{I_0} \right) \, C }$$
$$t ~=~ \ln\left( \frac{I(t)}{I_0} \right) \, R \, C$$
Discharge current
$$ I(t) $$ Unit $$ \mathrm{A} $$
The current that flows when the capacitor is discharged. The current does not drop to zero immediately, but reaches zero after a certain time.
Initial current
$$ I_0 $$ Unit $$ \mathrm{A} $$
The current at time \( t = 0 \). Its value is given by the applied source voltage \(U_0\) and the resistance \(R\): \( I_0 ~=~ \frac{U_0}{R}\).
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 \( 1 \, \mathrm{V} \). The capacitance has an effect on how fast the capacitor can discharge.
Electrical Resistance
$$ \class{brown}{R} $$ Unit $$ \mathrm{\Omega} $$
Resistor with resistance \( R \) connected in series with the capacitor. The resistance has an effect on how fast the capacitor can discharge.
Time
$$ t $$ Unit $$ \mathrm{s} $$
At the time \(t = 0\) of the discharge process, the current has the value: \( I(0) = - I_0\). With time, the discharge current decreases to zero.