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Capacitors in parallel is a type of multiple capacitor connection. Multiple capacitor connections are known to operate as a single equivalent capacitor. The total capacitance of this equivalent single capacitor is determined by the individual capacitors as well as the connections between them. There are two types of capacitor connections that are commonly used: Series connection and Parallel connection.
Also Read: Combination of Capacitors
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Key Takeaways: Capacitor, Capacitance, Parallel connection, Series connection, Electric Potential, AC & DC generator, passive electrical component, Electric field, condenser
What is a Capacitor?
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A capacitor is an electrical energy storage device that operates in an electric field. It's a two-terminal passive electrical component. Earlier, the capacitor was known as a condenser. Condenser microphones are also sometimes known as capacitor microphones.
Capacitors come in a variety of shapes and sizes, and there are many different types of capacitors in use. Although a capacitor has less storage capacity than a battery, it charges and discharges quickly. There are two foils in a capacitor: cathode foil (-) and anode foil (+).
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Capacitance is the term used to describe the effect of a capacitor. The ratio of the magnitude of the charge to the magnitude of the potential difference between two conductors is the capacitance of a capacitor.
C= Q /V
The SI unit of capacitance is the farad (F)
1 farad= 1 Coulomb / 1volt
The video below explains this:
Capacitance Detailed Video Explanation:
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Capacitor in Parallel
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There are two ways to link capacitors which are series connection and parallel connection. When capacitors are connected in series, they are connected one after the other in a chain. The capacitance is lower in series.
The capacitors are said to be connected in parallel when they are connected between two common locations. The capacitance is doubled when the plates are connected in parallel because the size of the plates is doubled. As a result, by connecting capacitors in parallel, we can increase the capacitance.
The total capacitance may be simply estimated for both series and parallel capacitor connections. The following are some of the reasons why capacitors are connected in parallel:
- Higher capacitance values
- To deliver an accurate value that would otherwise be unavailable
- On a printed circuit board, to create a dispersed capacitance
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Formula of Capacitor in Parallel
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Let C1, C2, C3, C4 be the capacitance of four parallel capacitor plates in the circuit diagram. C1, C2, C3, and C4 are all connected in a parallel combination.
Capacitors in Parallel
The potential difference across each capacitor in a parallel configuration of capacitors will be the same if the voltage V is applied to the circuit. However, the charge on each capacitor varies.
Current flows from the positive terminal of the battery to the junction when it is connected to the circuit. As a result, the charge in the circuit begins to flow.
This charge is divided into four parts: Q1, Q2, Q3, and Q4. The charge on one plate of the capacitor C1 is +Q1, whereas the charge on the other plate of the capacitor C1 is -Q1.
The charge on one plate of the capacitor C2 is +Q2, while the charge on the other plate is -Q2.
Similarly, the capacitor C3 contains charge +Q3 on one plate and charge -Q3 on the other plate due to induction.
Similarly, one plate of the C4 capacitor has charge +Q4 and the 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
When four capacitors are linked in parallel, Cp is used to express the equivalent capacitance.
The equivalent capacitance is if three capacitors are connected in parallel.
Cp = C1 + C2 + C3
The equivalent capacitance is if n capacitors are linked in parallel.
Cp = C1 + C2 + C3 +………. +Cn
The total capacitance of a series of parallel capacitors is simply the sum of their capacitance values. The number of capacitors that can be linked in parallel is theoretically unlimited. But, depending on the application, area, and other physical constraints, there will undoubtedly be practical limitations.
Application of Parallel Capacitor
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Arranging various capacitors in parallel allows the resultant circuit to store more energy because the equivalent capacitance of all capacitors involved is the sum of their capacitances. Using capacitors in parallel gives you more options when it comes to how you may use them. The following apps make use of this effect:
- Parallel capacitors are sometimes used in the DC power supply to better filter the output signal and eliminate AC ripple.
- With inductive loads, energy storage capacitor banks are used for power factor adjustment.
- In the automobile industry, capacitive storage banks are utilized for regenerative braking in large vehicles such as trams and hybrid cars.
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Things to Remember
- A capacitor is an electrical device that stores electrical energy in a passive manner.
- There are two terminals on a capacitor.
- Capacitance is defined as the ratio of a system's change in electric charge to its corresponding change in electric potential.
- There are two ways to link capacitors- series connection and parallel connection.
- In a series connection, capacitors are connected one after the other in a chain.
- The capacitance is lower in series connections.
- The capacitors are said to be connected in parallel when they are connected between two common locations.
- The capacitance is doubled when the plates are connected in parallel because the size of the plates is doubled.
- The formula to calculate the equivalent capacitance for n capacitors that are linked in parallel is-
Cp = C1 + C2 + C3 +………. +Cn
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Sample Questions
Ques: The given graph shows the variation of charge q versus potential difference V for two capacitors C1 and C2. Both the capacitors” have the same plate separation but the plate area of C2 is greater than that of C1. Which line (A or B) corresponds to and why? (All India 2014 C, 2 Marks)
Ans: 
From the graph, we can see the slope q/v for Capacitance is greater for A than B.
Also according to the given conditions, the capacitance εA/d i.e C ∝ A.
So, Capacitance is larger for the C2 because the area of its plates is larger and d for the two capacitors is the same. Hence, A represents C2.
Ques: A metal plate is introduced between the plates of a charged parallel plate capacitor. What is its effect on the capacitance of the capacitor? (Foreign 2009, 1 Mark)
Ans: If a metal plate is introduced between the plates of a charged parallel plate capacitor then the capacitance of the parallel plate capacitor will become infinite.
Ques: What is Parallel Plate Capacitance? (2 Marks)
Ans: Two metal plates are arranged parallel to each other and separated by a distance in a parallel plate capacitor.
Assume P1 and P2 are two metal plates. When P1 is charged, it should have a positive charge.
C = Q / V is the formula for capacitance, where Q is the charge and V is the potential.
Due to induction, if the other plate P2 is kept parallel to P1, the inner surface of the plate P2 will have charge -Q and the outer surface of the plate P2 will have charge +Q.
Ques: A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor. (All India 2014, 2 Marks)
Ans: 
Ques: Two parallel plate capacitors of capacitances C1 and C2 such that C1 =2C2 are connected across a battery of V volt as shown in the figure Initially, the key (k) is kept closed to fully charge the capacitors. The key is now thrown open and a dielectric slab of dielectric constant K is inserted in the two capacitors to completely fill the gap between the plates. Find the ratio of (i) the net capacitance and (ii) the energies stored in the combination before and after the introduction of the dielectric slab. (Delhi 2014 C, 2 Marks)
Ans: Before the slab is inserted, the net capacitance of the circuit is
C =C1+C2 = 2C2+C2 = 3C2 (as they are in parallel)
Energy stored U= ½ CV2 = 3/2C2V2
After the slab is inserted, C1 becomes C1′ = KC1 and C2 becomes C2′=KC2
Now the net capacitance C′=C1′+C2′=KC1+KC2 = K(C1+C2) = 3KC2
When the switch is opened, but the capacitors are fully charged by voltage V and the energy stored U′=1/2C′V2 = 3/2KC2V2
∴U′/U = [(3/2)KC2V2.] / [(3/2)C2V2] = 1/K
Ques: A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate capacitor, but has the thickness d/2, where d is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor. (Delhi 2013, 2 Marks)
Ans: Initially when there is vacuum between the two plates, the capacitance of the capacitor is
C0 = ε0A/d
Where,
A= area of parallel plates
Suppose that the capacitor is connected to a battery, an electric field E0 is produced.
now if we insert the dielectric slab of thickness t=d/2 the electric field reduces to E.
If we insert the dielectric slab of thickness t. Then
t = d2 the electric field reduces to E.
If V be the potential difference between the plates of the capacitor, then
Ques: Two identical parallel plate (air) capacitors C1 and C2 have capacitance C each. The space between their plates is now filled with dielectrics as shown in the figure. If the two capacitors still have equal capacitance, they obtain the relation between dielectric constants K, K1 and K2. (Foreign 2011, 2 Marks)
Ans:
Ques: Three Capacitors 10, 20, 25 μF are Connected in Parallel with a 250V Supply. Calculate the Equivalent Capacitance. (3 Marks)
Ans: Given that:
C1= 10μF = 10 ×10-6 F
C2= 20μF = 20 × 10-6 F
C3 = 25μF = 25 × 10-6 F
The equivalent capacitance of a parallel combination is,
Cp= C1 + C2 + C3
Cp = 10 + 20 + 25
Cp = 55 μF
Ques: Two Condensers of Capacities 10 μF and 25 μF are Charged to 12V and 24V respectively. What is the Common Potential When they are Connected in Parallel? (3 Marks)
Ans: Given that:
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
The equivalent capacitance of a parallel combination is,
Cp = C1 + C2 = 10 + 25 = 35 μ
If V is common potential,
Q = CV
V= Q/C
V= 720/35 = 20.57 V
Ques: A parallel plate* capacitor is charged by a battery. After some time, the battery is disconnected and a dielectric slab of dielectric constant K is inserted between the plates. How would (i)the electric field between the plates (ii)the energy stored in the capacitor be affected? Justify your answer. (All India 2009, 3 Marks)
Ans: (i) The total charge on the capacitor remains conserved after the dielectric slab is introduced. Also, the capacitance of the capacitor increases to K times of original values.
(ii) 
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