Series Combination of Capacitors

The capacitor is a device or a passive electronic component with two terminals that store electrical energy in an electric field. The effect marked by the capacitor is the capacitance of the capacitor. There are two basic types of combinations of capacitors, i.e. series and parallel combinations of the capacitor. There is a regular arrangement of capacitors  In a series combination that means one after another. On the other hand, a parallel plate capacitor comprises two metal plates arranged parallely at some distance. This distance comprises any dielectric medium. Many capacitors join together to form a single equivalent capacitor whose capacitance depends upon the individual capacitors and their connection method. We can quickly determine the capacitance by using the formulas. Let’s study the formula of a series capacitor and its solved examples.

Derivation of the Formula of Series Capacitor

The capacitance of any capacitor is connected to the voltage and charge with the given formula:

C= Q/V

Where Q= charge and

V= voltage

C=capacitance.

Now, V=Q/C

The voltage of each individual capacitor (Q remains the same) of the series capacitors are:

V1=Q/C1, V2=Q/C2, V3=Q/C3, V4=Q/C4…

The total voltage will be equal to,

V= V1+ V2+ V3+ V4…

Total Capacitance, say CS , will be:

Q/Cs= Q/C1 +Q/C2+Q/C3 +Q/C4…

On solving, we get:

1/Cs= 1/C1 +1/C2+1/C3 +1/C4…

Thus, the reciprocal of total capacitance of the capacitors, when arranged in series, will be the sum of reciprocals of the individual capacitance of capacitors.

Factors on which Capacitance Depends

The factors that cause either the increase or decrease of capacitance (series and parallel combination of capacitors) are as follows:

• The plate area is directly proportional to the capacitance, which means on increasing the plate area (other factors remaining the same), the capacitance also increases.
• Spacing between the plates is inversely proportional to the capacitance, which means the capacitance will decrease on increasing the plate space.
• Other factors remaining constant, the greater permittivity of the dielectric substance increases the capacitance and vice versa.

Features of Series Combination of Capacitors

Some of the features of the series combination of capacitors are as follows:

• There is only one path in a series combination to proceed from one point to another.
• The individual capacitors have the same charge on each capacitor in the series capacitor.
• The Series Combination of Capacitors always obeys the laws of conservation.
• The potential difference will be inversely proportional to its capacitance, i.e. contrasting parallel capacitance.

Parallel Plate Capacitor

A parallel plate capacitor comprises two metal plates arranged in a parallel manner at some distance. This distance includes any dielectric medium (an insulating medium that cannot conduct electric current). Some examples of this dielectric medium include air, vacuum, mica, paper wool, electrolytic gel, glass etc. The dielectric medium is non-conducting. However, under the effect of the electric field, they do get polarised. This causes the production of dipoles and therefore, both charges, i.e. a negative and a positive charge, get deposited over the plates of the capacitor.

The Formula for Parallel Plate Capacitor

Suppose a parallel-plate capacitor comprising two metallic plates has an area of A. Moreover, the distance separating these two plates is d. The formula for a parallel plate capacitor will be as follows:

C= kε₀Ad

Here,ε₀ =permittivity of space, whose value is 8.854 × 10−12 F/m

k =relative permittivity of dielectric material

d= distance of separation between the plates

A= area of plates

Solved Questions on Series Combination of Capacitors

Q 1- What will be the total capacitance of any capacitor given that each of its three individual capacitors has a capacitance of 1.000, 8.000 and 5.000 μ F. These three capacitors are connected in series combinations.

Solution:

We know that the capacitance of a capacitor connected in a series is equal to the sum of the reciprocal of each capacitor of that series.

Therefore, by using the formula,

1/Cs= 1/C1 +1/C2+1/C3

Substituting the values in the formula, we get:

1Cs= 1/1.000 + 1/8.000 +1/5.000 μ F.

1/Cs= 1.325/ μ F.

Cs= 0.755 μ F.

Q 2- In a series combination, there are two capacitors, i.e. C1 and C2. The capacitance of the first capacitor is 6 μ. In contrast, the capacitance of another capacitor is 3 μ F. Determine their equivalent capacitance using the formula of the series capacitor.

Solution:

We know that the capacitance of a capacitor connected in a series is equal to the sum of the reciprocal of each capacitor of that series.

Therefore, by using the formula,

1/Cs= 1/C1 +1/C2

1/Cs= 1/6 +1/3 μ F

Answer= 2 μ F

Conclusion

There are two basic types of combinations of capacitors, i.e. series and parallel combinations of the capacitor. In a series combination of capacitors, each capacitor is connected one after another. On the other hand, the two plates are arranged in parallel with dielectric material in between in a parallel capacitor. The reciprocal of total capacitance of the capacitors, when arranged in series, will be the sum of reciprocals of the individual capacitance of capacitors. The series capacitors can reduce the line voltage drop and improvise  voltage regulation. There is only one path in a series combination to proceed from one point to another, and the individual capacitors have the same charge on each capacitor. The capacitors in series combination also obey the laws of conservation of energy.