A Brief Note on Parallel Combination of Capacitors

Capacitors can be defined as the devices used to trap and store electric energy in an electric field. They are commonly used in electrical circuits to help regulate the flow of electricity. Capacitors consist of two conducting plates separated by an insulator, typically air. When voltage is applied to the capacitor, the electric field builds up between the plates, storing electrical energy. Here, we will learn about the parallel combination of capacitors and obtain the formula for the same. 

What is the combination of capacitors?

Every capacitor will have a capacitance. The capacitance (ability to store charge) is a function of the size and shape of the plates, as well as the distance between them. The setup where the capacitors are connected in parallel is known as a parallel combination of capacitors.

To obtain a resultant capacitance, when several capacitors with different capacitance are combined is said to be the combination of the capacitor. 

In simple terms, say to obtain the required value of C, we combine different capacitors with different capacitances like C1, C2, C3, and so on; this combination will be known as the combination of capacitors. 

The required value of the resultant capacitance defines the type of capacitor combinations. 

Methods of the combination of capacitors

There are different ways to combine capacitors. To apply a potential difference (V) and charge the metal plates (Q), the combination is attached to a power supply which is generally a battery. The combination’s equivalent capacitance amidst the two different points can be denoted as:

 C=Q/V

 Below are the two widely used methods of the combination of capacitors include:

• Parallel combination

• Series combination

The parallel combination of a capacitor

When both the capacitor’s terminals are combined with each terminal of other capacitors, the combination of such various parallel plate capacitors is called the parallel combination of a capacitor.

The combination of multiple capacitors can result in interesting effects, such as voltage doubler or frequency multiplier circuits. When capacitors are placed in parallel, the total capacitance will be the sum of all individual capacitances. This is because capacitors store charge, and when placed in parallel, each capacitor will have the opportunity to store a portion of the total charge. In electrical systems, capacitors are often placed in parallel to increase the current handling capacity of a circuit.

Let us learn with an example

Suppose combining three capacitors, each having a distinct capacitance, parallelly, and this parallel combination is applied a potential difference. 

In a parallel combination of a capacitor, every capacitor is directly connected to the battery or the power supply source. In this case, the potential difference between every capacitor is the same as the potential difference applied (V).

When we apply a potential difference to the capacitor’s plates, they start getting charged. The difference in capacitance leads to a difference in the charge on each capacitor. 

In the above diagram, we can see the combination of different parallel plate capacitors. When one parallel plate capacitor is connected to another, the combination is called a parallel combination.

For instance, if we connect VDC (supply voltage) to the parallel combination of the capacitors C1, C2, and C3, the voltage remains the same in each capacitance.

For capacitor C1,

Voltage=V1

The charge stored in the capacitor = Q1

The current running through the capacitor =I1

For capacitor C2,

Voltage=V2

The charge stored in the capacitor = Q2

The current running through the capacitor =I2

For capacitor C3,

Voltage=V3

The charge stored in the capacitor = Q3

The current running through the capacitor =I3

As the voltage across the parallel combination of the capacitor remains the same. Therefore, the voltage applied can be denoted as,

VDC= V1 =V2=V3

As the figure demonstrates, the positive terminal of the battery is connected to the top plates of every parallel plate capacitor, while the negative terminal is attached to the bottom parallel plate capacitor combination. Furthermore, all the top side plates of the first capacitor C1, the second capacitor C2 and third capacitor C3 are connected, while the bottom side plates of the first capacitor C1, the second capacitor C2 and third capacitor C3 are connected.

In the parallel combination of a capacitor, Ceq is the sum of all the capacitors’ capacitance values.

Total capacitance in parallel, Ceq, can be calculated as follows:

Ceq= C1+C2+C3+…+Cn

Therefore, the equation in the above example becomes;

Ceq= C1+C2=C3

Key points of the parallel combination of capacitors

• The potential across each capacitor is the same in the parallel combination of capacitors.

• The charge is proportional to the capacitor’s capacity and is different in each case.

Q ∝ C thus,

Q1=C1V

Q2=C2V

Q3=C3V

• The parallel combination abides by the law of conservation of charge

• Therefore,

           Q= Q1+Q2+Q3

            = C1V + C2V+ C3V

            = (C1+C2+C3) V

Equivalent capacitance can be shown as,

Ceq= Q/V = C1+C2+C3

Conclusion

The parallel combination of capacitors refers to the arrangement where several capacitors are connected in parallel. Both of the capacitors’ terminals are connected to each of the other capacitors’ terminals.

In a parallel combination of a capacitor, the equivalent capacitance always exceeds any individual capacitor’s capacitance. We use a parallel combination of capacitors to ensure efficient and more stable power systems in households or for commercial use. 

The voltage across the parallel combination of the capacitor remains the same. The parallel combination is often seen in the house’s electrical wiring, computer hardware, and so on.