In the first branch, containing the 4µF and 2µF capacitors, the series capacitance is 1.33µF. And in the second branch, containing the 3µF and 1µF capaictors, the series capacitance is 0.75µF. Now in total, the circuit has 3 capacitances in parallel, 1.33µF, 0.75µF, and 6µF.
The series combination of two or three capacitors resembles a single capacitor with a smaller capacitance. Generally, any number of capacitors connected in series is equivalent to one capacitor whose capacitance (called the equivalent capacitance) is smaller than the smallest of the capacitances in the series combination.
Capacitors can be connected in series: The equivalent capacitance for series-connected capacitors can be calculated as For the special case with two capacitors in series - the capacitance can be expressed as - or transformed to The equivalent capacitance of two capacitors with capacitance 10 μF and 20 μF can be calculated as in parallel in series
Solving q = 1 1 C1+ 1 C2 V q = 1 1 C 1 + 1 C 2 V for the ratio q V q V yields q V = 1 1 C1+ 1 C2 q V = 1 1 C 1 + 1 C 2 so our equivalent capacitance for two capacitors in series is Cs = 1 1 C1+ 1 C2 C s = 1 1 C 1 + 1 C 2 By logical induction, we can extend this argument to cover any number of capacitors in series with each other, obtaining:
These two basic combinations, series and parallel, can also be used as part of more complex connections. Figure 8.3.1 8.3. 1 illustrates a series combination of three capacitors, arranged in a row within the circuit. As for any capacitor, the capacitance of the combination is related to both charge and voltage:
The equivalent capacitor for a parallel connection has an effectively larger plate area and, thus, a larger capacitance, as illustrated in Figure 19.6.2 19.6. 2 (b). Total capacitance in parallel Cp = C1 +C2 +C3 + … C p = C 1 + C 2 + C 3 + … More complicated connections of capacitors can sometimes be combinations of series and parallel.