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= \[\frac {Q} {V}\]
The SI unit of capacitance is the farad (F)
1 farad= \[\frac {1Coulomb} {1volt}\]
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 a 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 a parallel combination of capacitors, we get more capacitance.
Capacitors in the Parallel Formula
Working of Capacitors in Parallel
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
Advantages of using Capacitors in Parallel
Connecting capacitors in parallel results in more energy being stored by the circuit compared to a system where the capacitors are connected in a series. This is because the total capacitance of the system is the sum of the individual capacitance of all the capacitors connected in parallel.
In complicated capacitor banks, which operate with extremely high levels of capacitance values have observed a better voltage balance between capacitor bundles when connected in parallel and hence a reduction in the number of balancing resistors to be used in the system.
This saves money as it costs a lot less compared to when capacitors are connected in series because more balancing resistors are needed. In turn, more power losses are observed due to more current paths as the construction of the system becomes more complex with more use of balancing resistors.
Even after saving costs and storing more energy, this system is considered unsafe for use in industry. Students must read on to find out why.
Disadvantages of using Capacitors in Parallel
By now, the students are aware that the same voltage is applied to all capacitors in a parallel circuit. This means that even the capacitors with the highest rated voltage will only be as high as the lowest-rated one out of all capacitors.
For example, if a capacitor rated at 200V is connected to a series of capacitors rated at 500V in parallel, the maximum voltage rating of the whole rating will only be 200V even if most capacitors in the system were rated at 500V, just because of one capacitor rated at 200V.
Capacitors in parallel are capable of storing really huge amounts of energy and are also able to release that stored energy in a very little amount of time. If shorted out by accident, this could be dangerous and prone to injuries and failure due to heavy damage to the electrical wiring. It is because of high chances of safety issues, this system is NOT recommended for use in industry and is mostly avoided by professionals.
In complex capacitor banks layout, if one capacitor fails, the capacitors in the remaining bank would have to bear the full bus voltage. This could lead to the failure of the entire capacitor bank as the remaining capacitors would eventually fail.
This is avoidable when capacitors are connected in series because even if one capacitor fails, the remaining capacitors in the bank remain unaffected.
Students can learn more about real-life applications of electric systems used heavily across multiple industries on the Vedantu website and app.
FAQs on Capacitors in Parallel
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 plastic film and its dielectric.
Ceramic capacitor - This type of capacitor has two or more alternating layers of ceramic and metal. They have high stability and 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 P1 and P2. Let the charge on P1 when it is charged be positive.
Capacitance is given by, C = \[\frac {Q} {V}\] where Q is the charge and V is the potential
Now the other plate P2 is kept parallel to P1 then the inner surface of the plate P2 will have charge -Q and the outer surface of the plate P2 will have charge +Q this is due to induction.
3. What is a Dielectric?
A capacitor in its simplest form is made up of two or more parallel conductive plates that are electrically separated by a dielectric to make sure the plates are not connected or touching each other.
Dielectric material depends on the type of capacitor used and can be plastic, liquid form gel, mica, waxed paper or ceramic. Dielectric material depends on the type of capacitor used and can be plastic, liquid form gel, mica, waxed paper or ceramic.
A dielectric is a material that is a type of insulator that gets polarized upon contact with an electric field. Hence, it is a poor conductor of electricity, but an efficient supporter of electrostatic fields. Due to the dielectric's insulating nature, direct current cannot flow through it which allows voltage to be present across the metal plates in the form of electric charge.
Students can understand the intricate construction of electrical devices like capacitors of different types, inductors and so on along with their purposes, comparisons and industry use on Vedantu. Lessons related to electrostatic topics in physics are available to students to download for free from the Vedantu website and app.
4. Is capacitor and condenser the same thing?
Yes in this topic's context, capacitors and condensers are one and the same thing. The capacitor is the term that simply replaced the term condenser because both these terms achieve the same purpose.
A capacitor stores a large amount of voltage at relatively speaking, low electrical pressure. This makes the working theme of a capacitor exactly the same as a 'condenser'. For our topic, there is no difference in their meaning, working or definition. The capacitor has just been the newer term for a condenser which was only used until 1926.
5. What is the difference between a capacitor and a conductor?
A capacitor is used to store charge for a given amount of time, whereas a conductor is capable of transferring electric charge due to the possession of free charge carriers. A capacitor just stores charge, whereas a conductor allows free flow of charge.
A capacitor is a passive element in a circuit that is capable of storing electricity in the form of electrostatic charges, but an electrical conductor is a substance that is a carrier of current when a voltage is applied. Capacitors contain an insulating material called dielectric between metal plates. Whereas, there is no insulation/resistance or concept of dielectric in conductors.
