Parallel combination of capacitors
Figure below shows two capacitors connected in parallel between two points A and B
Right hand side plate of capacitors would be at same common potential VA. Similarly left hand side plates of capacitors would also be at same common potential VB.
Thus in this case potential difference VAB=VA-VB would be same for both the capacitors, and charges Q1 and Q2 on both the capacitors are not necessarily equal. So,
Q1=C1V and Q2=C2V
Thus charge stored is divided amongst both the capacitors in direct proportion to their capacitance.
Total charge on both the capacitors is,
Q=Q1+Q2
=V(C1+C2)
and
Q/V=C1+C2
So system is equivalent to a single capacitor of capacitance
C=Q/V
where,
When capacitors are connected in parallel their resultant capacitance C is the sum of their individual capacitances.
The value of equivalent capacitance of system is greater then the greatest individual one.
If there are number of capacitors connected in parallel then their equivalent capacitance would be
C=C1+C2+ C3...........
Series combination of capacitors
Figure 7 below shows two capacitors connected in series combination between points A and B.
Both the points A and B are maintained at constant potential difference VAB.
In series combination of capacitors right hand plate of first capacitor is connected to left hand plate of next capacitor and combination may be extended foe any number of capacitors.
In series combination of capacitors all the capacitors would have same charge.
Now potential difference across individual capacitors are given by
VAR=Q/C1
and,
VRB=Q/C2
Sum of VAR and VRB would be equal to applied potential difference V so,
V=VAB=VAR+VRB
=Q(1/C1 + 1/C2)
i.e., resultant capacitance of series combination C=Q/V, is the ratio of charge to total potential difference across the two capacitors connected in series.
So, from equation 12 we say that to find resultant capacitance of capacitors connected in series, we need to add reciprocals of their individual capacitances and C is always less then the smallest individual capacitance.
Result in equation 12 can be summarized for any number of capacitors i.e.,
1/C=1/C1+1/C2+1/C3+......
