What is grouping of Capacitors?

Capacitors can be arranged in two different ways.

1. Capacitors in Series
2. Capacitors in Parallel

Capacitors in Series :– Capacitors are said to be in series combination between the two points whenever there will be a single path through which we can reach from one point to another.
You can see the arrangement of capacitors in series in the figure drawn below:

In the figure above we have placed three capacitors named C1,C 2, C3 in series. V is the potential difference along the circuit.

If we apply positive charge to the plate present on the left side of first capacitor C1. Then due to the phenomenon of Electrostatic Induction that we have read earlier, an induced negative charge will come on the plate present on the right side of the capacitor. The positive charge which we have applied on the left plate of the capacitor C1 will flow towards the other capacitors and in a short time all the left side plates of the capacitors present in series will get positive charge. Capacitors in the series may or may not be of same capacity. Potential differences of the capacitors will vary. Below given are the equations of different capacitors having different potential differences.
V1=Q/C1 ,
V2=Q/C2 ,
V3=Q/C3

Let us assume the total capacitance of the whole circuit to be c_s, then
V=Q/C_s
AS V=V1 +V2 +V3
Therefore
Q/C_s= Q/C1 +Q/C2 +Q/C3
= Q(1/C1 + 1/C2 + 1/C3)
1/C_s= 1/C1 +1/C2 +1/C3 ——2.11

The above equation is only for three capacitors which are connected in series. But if we talk about n capacitors that are connected in series then the equation will be:

1/C_s=_i=1 ⁱ⁼ⁿ 1/C_i

Above equation says that , the reciprocal of n no of capacitance of capacitors connected in series is equal to the total of the reciprocals of the Capacitances of individual capacitors.

Capacitors in Parallel :- Capacitors are said to be connected in parallel if we can reach from one point to different points through different paths.

The figure below is showing the capacitors connected in parallel. Let us suppose that three capacitors having capacitance C₁, C₂ , and C₃ are connected in parallel respectively. The potential difference that we have applied along the combination is V.

So according to the above data the three equation formed will be :
Q₁=C₁V,
Q₂=C₂V,
Q₃=C₃V.
As we know that the sum of the total charge in the circuit will be
Q= Q₁ +Q ₂+ Q₃+ Q₄
Suppose that C_p will be the total capacitance along the circuit :
Then Q=C_pV
By substituting the values in the above equations we get:
C ₁ V= C ₁ V+ C ₂V + C₃V
Taking V common from the above equations
=(C₁ +C₂+C₃)V
So, the general expression which gives the resultant equation when n capacitors connected in parallel is:
C_p=_i=1
C _i

So according to the above equation, the capacitance of the circuit with no of capacitances connected in parallel is the total sum of all the capacitances of the individual capacitors connected in parallel.