Voltage across the capacitor
voltage across the capacitor
The charge "Q" of the capacitor is related to the potential difference by the following relation:
\[dQ=CdU_{c}\]
and the current i to the quantity of electricity (or charge) is given by the relation
\[i=\frac{dQ}{dt}\]
The first relationship can be written as a function of the output voltage “Uc" as follows
\[E=RC\frac{U_{c}}{dt}+U_{c} \Rightarrow \frac{R}{RC} = \frac{d U_{c}}{dt} +\frac{U_{c}}{RC}\]
Under the following initial conditions, t = 0; Uc = 0, the voltage across the capacitor is the solution to the above differential equation, and is written in the form:
\[U_{c}(t)=E(1-e^{-t/RC})\]
and the current of the capacitor is
\[i(t)=\frac{E}{R}e^{-t/RC}\]