Capacitors in series draw the same current and store the same amount of electrical charge irrespective of the capacitance value. In this article, we will learn the series connection of capacitors and will also derive the expressions of their equivalent capacitance.
Figure 8.3.1 8.3. 1: (a) Three capacitors are connected in series. The magnitude of the charge on each plate is Q. (b) The network of capacitors in (a) is equivalent to one capacitor that has a smaller capacitance than any of the individual capacitances in (a), and the charge on its plates is Q.
Thus, the total capacitance is less than any one of the individual capacitors’ capacitances. The formula for calculating the series total capacitance is the same form as for calculating parallel resistances: When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitors’ capacitances.
Thus, the equivalent capacitance of the capacitor connected in series is, 24/27 μF In the figure given below, three capacitors C1, C2, and C3 are connected in parallel to a voltage source of potential V. Deriving the equivalent capacitance for this case is relatively simple.
Note that in a series network of capacitors, the equivalent capacitance is always less than the smallest individual capacitance in the network. A parallel combination of three capacitors, with one plate of each capacitor connected to one side of the circuit and the other plate connected to the other side, is illustrated in Figure 8.12 (a).
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:
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Derive expressions for total capacitance in series and in parallel. Identify series and parallel parts in the combination of connection of capacitors. Calculate the effective capacitance in series and parallel given individual capacitances.
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