Series Combination of Capacitors
In the figure given below, three capacitors are connected in series with the battery of voltage V. Note that in the figure, opposite charges of equal magnitude flow and get accumulated on the plates of the capacitor. Conservation of charge principles requires that the charge that is accumulated on the plates of the capacitor must be equal in magnitude. The end result is a combination that resembles a single capacitor with an effective plate separation that is greater than that of individual capacitors, this equivalent capacitor is shown in the figure below. Large plate separation means smaller capacitance.
The derivation of relation for capacitors in series is explained below:
The relation for capacitance is given by,
C = Q/V
It can be rewritten as,
V = Q/C
The voltages across individual capacitors will be,
V1 = Q/C1 , V2 = Q/C2, V3 = Q/C3
The total voltage across all the capacitors will be,
V = V1 + V2 + V3
substituting the expressions for individual voltages,
V = Q/C1 +Q/C2 + Q/C3
Let the equivalent capacitance be C,
Q/C = Q/C1 +Q/C2 + Q/C3
Upon Simplifying the above equation, the relation becomes,
In general for capacitors C1, C2, C3,…
Example of Capacitor Connected in Series Combination
Let’s take four capacitors of capacitance 2 μF, 6 μF, 8 μF, and 3 μF connected in series then find the equivalent capacitance of the circuit.
Solution:
Given
- C1 = 2 μF
- C2 = 6 μF
- C3 = 8 μF
- C4 = 3 μF
Equivalent capacitance of the capacitor in Parallel Combination
1/Ceq = 1/C1 + 1/C2 + 1/C3 + 1/C4
1/Ceq = 1/2 + 1/6 + 1/8 + 1/3
1/Ceq = (12 + 4 + 3 + 8)/24 = 27/ 24
Ceq = 24/27 μF
Thus, the equivalent capacitance of the capacitor connected in series is, 24/27 μF
Capacitors in Series and Parallel
Capacitors are special devices that can hold electric charges for instantaneous release in an electric circuit. We can easily connect various capacitors together as we connected the resistor together. The capacitor can be connected in series or parallel combinations and can be connected as a mix of both.
In this article, we will learn about capacitors connected in series and parallel, their examples, and others in detail.