Formula: Charging Capacitor Capacitor current Capacitance Electrical Resistance Time
$$I(t) ~=~ I_0 \, \mathrm{e}^{-\frac{t}{R\,C}}$$
$$I(t) ~=~ I_0 \, \mathrm{e}^{-\frac{t}{R\,C}}$$
$$I_0 ~=~ I(t) \, \mathrm{e}^{\frac{t}{R\,C}}$$
$$C ~=~ - \frac{ t }{ \ln\left( \frac{I(t)}{I_0} \right) \, R }$$
$$R ~=~ - \frac{ t }{ \ln\left( \frac{I(t)}{I_0} \right) \, C }$$
$$t ~=~ - \ln\left( \frac{I(t)}{I_0} \right) \, R \, C$$
Capacitor current
$$ I(t) $$ Unit $$ \mathrm{A} $$
Capacitor current is the electric current that flows into the plate of the capacitor and thus builds up a voltage on the capacitor. This capacitor current decreases exponentially with time during the charging process, while the capacitor voltage \( U(t) \) increases exponentially.
Charging current
$$ I_0 $$ Unit $$ \mathrm{A} $$
Charging current is the initial current that flows into the capacitor plate at time \( t = 0 \). Its value is given by the applied source voltage.
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 \( 1 \, \text{V} \).
Electrical Resistance
$$ \class{brown}{R} $$ Unit $$ \mathrm{\Omega} = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{A}^2 \, \mathrm{s}^3 } $$
Resistor with resistance \( R \) connected in series with the capacitor. The resistor has an influence on how fast the capacitor can charge.
Time
$$ t $$ Unit $$ \mathrm{s} $$
After the source voltage \(U_0\) is applied (switch is closed), the capacitor starts to charge. The charging current starts to flow through the circuit and decays over time \(t\).