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:
(c) The assumption that the capacitors were hooked up in parallel, rather than in series, was incorrect. A parallel connection always produces a greater capacitance, while here a smaller capacitance was assumed. This could happen only if the capacitors are connected in series.
Total capacitance in parallel Cp = C1 +C2 +C3 + … C p = C 1 + C 2 + C 3 + … If a circuit contains a combination of capacitors in series and parallel, identify series and parallel parts, compute their capacitances, and then find the total.
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.
Find the net capacitance for three capacitors connected in parallel, given their individual capacitances are 1.0μF,5.0μF, and8.0μF. 1.0 μ F, 5.0 μ F, and 8.0 μ F. Because there are only three capacitors in this network, we can find the equivalent capacitance by using Equation 8.8 with three terms.
Series connections produce a total capacitance that is less than that of any of the individual capacitors. We can find an expression for the total capacitance by considering the voltage across the individual capacitors shown in Figure 19.6.1 19.6. 1. Solving C = Q V C = Q V for V V gives V = Q C V = Q C.