Capacitors in Parallel Notes

A capacitor is a device that stores energy (electrical) by storing the charge. A capacitor has two terminals. It is a passive electrical component. A capacitor was earlier known as a condenser. Compared to a battery, a capacitor has less storage but the charging and discharging are fast in the capacitor. Inside a capacitor, there are two foils, cathode foil (-), and anode foil (+). The effect of the capacitor is known as capacitance. The capacitance of a capacitor is the ratio of the magnitude of the charge to the magnitude of the potential difference between two conductors.

C= Q /V

The SI unit of capacitance is the farad (F)

1 farad= 1Coulomb / 1volt

Capacitors in Parallel

Capacitors can be connected in two types which are in series and in parallel. If capacitors are connected one after the other in the form of chain then it is in series. In series, the capacitance is less.

When the capacitors are connected between two common points they are called to be connected in parallel.

When the plates are connected in parallel the size of the plates gets doubled, because of that the capacitance is doubled. So in parallel combination of capacitors, we get more capacitance.

Capacitors in the Parallel Formula

Working of Capacitors in Parallel

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In the above circuit diagram, let C1, C2, C3, C4 be the capacitance of four parallel capacitor plates. C1, C2, C3, C4 are connected parallel to each other.

If the voltage V is applied to the circuit, therefore in a parallel combination of capacitors, the potential difference across each capacitor will be the same. But the charge on each capacitor is different.

When the battery is connected to the circuit the current flows from the positive terminal of the battery to the junction. So, the charge starts flowing in the circuit.

This charge is distributed as Q1, Q2, Q3, Q4. One plate of the capacitor C1 acquires charge +Q1 while the other plate of the capacitor C1 acquires charge -Q1. This is by induction.

One plate of the capacitor C2 has charge +Q2 while the other plate of the capacitor C2 has charge -Q2 this is also by induction.

Similarly, for the capacitor C3, one plate has charge +Q3 while the other plate of capacitor C3 has charge -Q3 by induction.

Similarly, for the C4 capacitor, one plate has charge +Q4 other plate has charge -Q4

Now according to the law of conservation of charge,

Q = Q1 + Q2 + Q3 + Q4 — (1)

We know that C = Q / V

Q = CV

Q1 = C1V

Q2 = C2V

Q3 = C3V

Q4 = C4V

Q = CpV — (2)

From equations (1) and (2) we can write,

CpV = C1V + C2V + C3V + C4V

CpV = (C1 + C2 + C3 + C4 ) V

Cp = C1 + C2 + C3 +C4

Cp is the expression for the equivalent capacitance when four capacitors are connected in parallel.

If there are three capacitors connected in parallel then the equivalent capacitance is,

Cp = C1 + C2 + C3

If there are n capacitors connected in parallel then the equivalent capacitance is,

Cp = C1 + C2 + C3 +………. +Cn

Solved Examples

1.Three Capacitors 10, 20, 25 μF are Connected in Parallel with a 250V Supply. Calculate the Equivalent Capacitance.

Solution-

C1= 10μF = 10 ×10-6 F

C2= 20μF = 20 × 10-6 F

C3 = 25μF = 25 × 10-6 F

Equivalent capacitance of a parallel combination is,

Cp= C1 + C2 + C3

Cp = 10 + 20 + 25

Cp = 55 μF

2. Two Condensers of Capacities 10 μF and 25 μF are Charged to 12 V and 24 V Respectively. What is the Common Potential When they are Connected in Parallel?

Solution-

C1= 10 μF

C2= 25 μF

V1 = 12 V

V2 = 24 V

V=?

Charge on 1st condenser,

Q1= C1V1 = 10 × 10-6 × 12 = 120 × 10-6 C

Charge on 2nd condenser,

Q2= C2V2 = 25 × 10-6 × 24 = 600 × 10-6 C

Total charge Q = Q1 + Q2 = 120 × 10-6 + 600 × 10-6

Q = 720 × 10-6 C

Equivalent capacitance of a parallel combination is,

Cp = C1 + C2 = 10 + 25 = 35 μF

If V is common potential,

Q = CV

V= Q/C

V= 720/35 = 20.57 V

FAQ (Frequently Asked Questions)

1.Explain Different Types of Capacitors.

There are many types of capacitors available in the market some of them are,

Variable capacitor - In this type of capacitor, we can vary the capacitance value electronically. They are mostly used in LC circuits.

Trimmer capacitor - It is a non-polarized capacitor.

Film capacitor - It is a capacitor with an insulating a plastic film and it’s dielectric.

Ceramic capacitor - This type of capacitor has two or more alternating layers of ceramic and metal. They have high stability and they are non-polarized.

Polypropylene capacitor - In this capacitor, there is a polypropylene film as their dielectric. It is a high voltage working capacitor.

2.What is Parallel Plate Capacitance?

In a parallel plate capacitor, there are two metal plates placed parallel to each other separated by some distance.

Suppose we have two metal plates P_{1} and P_{2}. Let the charge on P_{1} when it is charged be positive.

Capacitance is given by, C = Q / V where Q is the charge and V is the potential

Now the other plate P_{2}_{ }is kept parallel to P_{1} then the inner surface of the plate P_{2} will have charge -Q and the outer surface of the plate P_{2}_{ }will have charge +Q this is due to induction.