Grouping of Capacitors
Capacitors are very important elements of electrical and electronic circuits. Sometimes a capacitance of a proper value may not be available. In such situations, grouping of capacitors helps to obtain desired (smaller or larger) value of capacitance with available capacitors.
Two most common capacitor groupings are:
- Series Grouping
- Parallel Grouping
Parallel Grouping of Capacitors
In parallel grouping, one plate of each capacitor is connected to one terminal and the other plate is connected to another terminal of a battery. In parallel combination, potential difference across each capacitor is the same.
q1 = C1V
q2 = C2V
q3 = C3V
q = q1 + q2 + q3
q = (C1 + C2 + C3)V
q = CpV
Cp = C1 + C2 + C3
The equivalent capacitance of a number of capacitors joined in parallel is equal to the sum of the individual capacitances.
Series Grouping of Capacitors
In the series combination of capacitors, the first plate of the first capacitor is connected to the electrical source. The second plate of the first capacitor is connected to the first plate of the second capacitor. The second plate of second capacitor is connected to first plate of the next capacitor of the combination and so on. The second plate of last capacitor of the combination is connected to the electrical source.
Each capacitor receives the same charge of magnitude q.
V1 = q/C1
V2 = q/C2
V3 = q/C3
V = V1 + V2 + V3
q/Cs = q(1/C1 + 1/C2 + 1/C3)
1/Cs = 1/C1 + 1/C2 + 1/C3
The reciprocal of equivalent capacitance of any number of capacitors connected in series is equal to the sum of the reciprocals of individual capacitances.