Electrical Engineering ⇒ Topic : Capacitance element

CAPACITANCE ELEMENT

In a pure capacitive circuit [Figure (a)], the time-domain relationship between current and voltage is given by

                        Figure (a) Pure capacitive circuit.

                             .......... (1)

The Laplace transform of Eq. (1) is given by

               ............ (2)

The initial voltage vo = v(0) with positive polarity on the side of the capacitor that opposes the charging current is considered. The equivalent circuit in s domain is shown in Figure (b).

Figure (b) Equivalent circuit of a pure capacitive element in s-domain (with positive polarity on the side of the capacitor that opposes the changing current).

If the initial voltage v_o = v(0-) with positive polarity on the side of the capacitor that assists the charging be taken into account, Eq. (2) becomes

                              .......... (3)

The equivalent circuit in s-domain is shown in Figure (c).

Figure (C) Equivalent circuit of a pure capacitive element in s-domain (with positive polarity on the side of the capacitor that assists the changing current).

Again from Eq. (2), it can be written that

                         ............. (4)

The equivalent circuit in s-domain is shown in Figure (D).

                      

Figure (D) Equivalent circuit of a pure capacitive element in s-domain.