The Combination Of Capacitors In Series And Parallel

Introduction

In physics, the combination of capacitors in series and parallel is an important chapter that needs a proper and detailed go through. This article can help you derive the expression for presenting the total capacitance present in series and parallel. Also, you can easily find out the parts present in the combination of capacitors in series and parallel. However, for the Series Combination of Capacitors, the charging current (Ic) that flows between the capacitors remains the same for all kinds of capacitors. The reason for the same is that the path of the flow of the currents remains the same. Nevertheless, the current can scatter within the capacitor in a parallel connection since the current flow does not remain at a constant stage.

What are capacitors, and how are they connected? 

The capacitor is the device or the active component that helps to store the energy in the form of electrical energy. However, this consists of two conductors that further remain detached with the help of the dielectric. 

The capacitance indicates the effects of the current stored in the device. Thus, it is commonly known as the ratio of electric charge to the voltage, where C= Q/V. Here, C is capacitance measured in Farad, Q is the Electric Charge measured in Coulombs, and V is the voltage measured in volts. 

Typically, the combination occurs in two ways: the series and the parallel method. However, several ways can be opted to perform the variety of capacitors in series and parallel. For instance, the combination is connected to a battery that can provide the potential difference. This difference can be indicated as V, including the charge of the plates, which is defined by Q. Thus, from the statement, it can be concluded as C= Q/V. 

Series Combination of Capacitors

Capacitors are connected to form the series combination of capacitors only when they connect in a single line. The capacitors in the series contain the same amount of electricity flowing through them as indicated by iT= i1 = i2 = i3. Thus, the individual capacitor will collect the same amount of electrical energy displayed as Q on its plates without knowing the capacitance. However, this happens when the charge stored by the plate of any capacitor comes from the side capacitor plate. Therefore, capacitors in the series contain the same amount of charge. 

Series Connection of Capacitors 

In the connection of capacitors in the series, the total value of the capacitance, denoted by CT, is calculated differently. Imagine a series of connections with C1, C2, and C3 capacitors, all connected in between two points A and B.

To derive the formula for capacitors in series, we need to apply Kirchhoff’s voltage law to the circuit

VAB= VC1 + VC2 + VC3

We know that  Q= C*V, or V= Q/C, so that

VC1 = QTC1,

 VC2 = QTC2,

 VC3 = QTC3

Further, rearranging the Q/C for individual capacitor Voltage VC in the above KVL equation,we can get the following capacitors in the series formula:

VAB= QTCT = QTC1 + QTC2 +QTC3

1CT = 1C1 + 1C2 +1C3

Parallel Combination of Capacitors

In a parallel combination of capacitors, the potential voltage difference among each of the capacitors remains the same. Let’s consider three capacitors of capacitance C1, C2 and C3 are connected in a parallel circuit and one voltage source VAB also attached in this circuit.

Since the capacitors in the parallel combination and  have a common voltage supply across them, which can be written as:

Vc1= Vc2= Vc3= Vab

When the capacitors are connected parallelly, the total capacitance CT in the circuit is the same as the sum of the individual capacitors when added together. Thus, we can see that the upper plate of the capacitor C1 is attached to the upper plate of C2. This is connected to the upper plate of C3, and in this way, it can go on. 

Similarly, the same is also accurate with the plates of the bottom capacitors. It is the same as the three sets of connected plates and equal to the single large plate, which further increases the effective plate area in m2. 

Also, as the capacitance, C is equal to the plate area (C= ε(A/d) ), the value of the C thus also increases. In simple terms, the total C is similar to the sum of all the particular capacitors present in the parallel capacitance. Also, both the combination of capacitors in series and parallel is also obtained in a similar manner. This further means that the equation for parallel capacitors are denoted as 

CT= C1 + C2 + C3

Conclusion

Thus, from the above information on the combination of capacitors in series and parallel, we found that several capacitors can be connected and used in various applications. Usually, there are two types of connections defined as the parallel and the series, which we can easily calculate to determine the total amount of capacitance. Also, to treat a more complex form of conductors, these two varieties of connections play a crucial role in storing the energy for further uses.