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Capacitors Grouping
In many electrical circuits, capacitors are to be grouped suitably to obtain the desired capacitance. Two most common modes of grouping of condensers are: series grouping and parallel grouping
Capacitors in series
The capacitors are said to be connected in series between two points when we can proceed from one point to the other only thought one path.
Let + Q units of charge be given to the left plate of C1. By electrostatic induction a charge – Q appears on inner side of right plate C1 and + Q appears on outer side of this plate. The + Q units of charge flow to left plate of C2 and so on* thus each capacitor receives the same charge of magnitude Q. as their capacities are different, therefore potential difference across the three capacitors are different:
V1 = Q / C1 V2 = Q / C2 V3 = Q / C3
If Ca is the total capacitance of the combination of a single capacitor that would acquire charge Q when potential difference across its terminals is V) then
V = Q /C
As total potential drop V across the combination is the sum of potential drops V1 V2 V3 across C1 C2 C3 respectively,
V = V1 + V2 + V3
∴ Q / C = Q / C1 + Q / C2 + Q / C3 + Q (1 / C1 + 1 / C2 + 1 / C3)
Or 1 / C = 1 / C1 + 1 / C2 + 1 / C3 V
If Q is the total charge on the parallel net work, then as total charges is the sum of charges on all capacitors.
Q = Q1 + Q3 + Q3 (2)
Let Cp be the equivalent capacitance in parallel (capacity of a single capacitor which would acquire the same total charge Q under the same potential difference V).
Q = Cp V
Putting these values in (12) we get
Cp V = C1 V + C2 V + C3 V = (C1 + C2 + C3) V
∴ Cp = C1 + C2 + C3
In general when n capacitors are connected in parallel, then
Cp = ∑ Ci
Equivalent capacitance of any number of capacitors joined in parallel is equal to sum of the individual capacitances. Obviously capacitance in parallel combination increases. Here Cp > the largest of C1, C2, C3….Cn
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