Combination of Capacitors – unite a large number of capacitors are being used in various electronic circuits and very often they have to be connected together. Generally, two methods are used for connecting them. One is known as parallel method and the other as series.
Parallel combination of capacitors
In this method left plates of all the capacitors are connected to one point and the right ones to another point (Fig. 15.14).
Fig. 15.14 parallel connection of capacitors.
This type of combination has the following characteristic features.
- If this combination of capacitors is connected with a battery of voltage V, the potential difference across each of the capacitors would be V (fig 15.15)
ig. 15. 15: potential difference across every capacitor is equal to the voltage of the battery.
- The battery supplies charge to each capacitor, the quantity of which depends upon the capacitance of the capacitor. In the circuit shown in fig 15.15, the charge on capacitor C1 is Q1 = C1V, the charge on capacitor C2 is Q2 = C2V and that on C3 is Q3 = C3v. if Q is the total charge supplied by the battery, then
Q = Q1 + Q2 + Q3
= C1V + C2V+C3V
= (C1 + C2 + C3) V…………(15.10)
Q/V = C1 + C2 + C3
- The parallel combination of capacitors, in a circuit, can be replaced by its equivalent capacitor of capacitance Ce such that
Ce = C1 + C2 + C3
If n capacitors are combined in parallel, the equivalent capacitance of the combination is given by
Ce = C1 + C2 + C3 + ……..+Cn ……… (15.11)
Series Combination of capacitors
In this method the capacitors are connected plate to plate, i.e., the right plaete of one capacitor is connected to the left plate of the next capacitor as shown in fig 15.16.
Fig 15.16 series connection of capacitors.
The following are the characteristic features of this combination:
- If this combination is connected to a battery, the charge on each capacitor would be the same. (Fig. 15.17). The battery supplies +Q charge to the left plate of the capacitor C1. Due to induction, -Q charge is induced on its right plate and +Q charge on the left plate of the capacitor has q charge.
fig. 15.17 amount of charge is same on each capacitor.
- The potential difference between the plates of each capacitor is according to its capacitance. In the circuit shown in fig. 15.17 the potential difference between the plates of capacitor C1 is V1=Q/C1, the potential difference across the plates of capacitor C2 is V2=Q/C2 and that across C3 is V3=Q/C3. It is the voltage V of the battery that is divided among the various capacitors. Hence
V = V1 +V2 +V3
- The series combination of capacitors in a circuit can be replaced by its equivalent capacitance Ce, the value of which is given by
If n capacitors are connected in series, the equivalent capacitance of the combination is given by
