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. What defines a parallel connection for capacitors in a circuit?
A parallel connection is one where the terminals of two or more capacitors are connected to the same two points in a circuit. This arrangement ensures that the potential difference (voltage) across each individual capacitor is identical to the voltage supplied by the source.
2. What is the formula for calculating the equivalent capacitance of capacitors in parallel?
The formula to find the equivalent or total capacitance (Cp) for capacitors connected in parallel is the simple sum of their individual capacitances. For 'n' capacitors, the formula is: Cp = C1 + C2 + C3 + ... + Cn. This means the total capacitance is always greater than the largest individual capacitance in the combination.
3. How are voltage and charge distributed among capacitors connected in parallel?
In a parallel capacitor circuit, the distribution follows two key rules:
- Voltage: The potential difference (voltage) across each capacitor is the same and is equal to the voltage of the power source connected to the circuit.
- Charge: The total charge supplied by the source is divided among the individual capacitors. The amount of charge stored on each capacitor (Q = CV) is directly proportional to its capacitance. The total charge is the sum of the charges on each capacitor: Qtotal = Q1 + Q2 + Q3.
4. Why does the total capacitance increase in a parallel combination?
The total capacitance increases because connecting capacitors in parallel effectively increases the total surface area available for charge storage. Think of it as combining the plate areas of all individual capacitors into one larger capacitor. Since capacitance is directly proportional to the plate area, a larger effective area allows the system to store more charge for the same applied voltage, leading to a higher overall capacitance.
5. What are the main differences between connecting capacitors in series versus in parallel?
The key differences relate to capacitance, voltage, and charge:
- Equivalent Capacitance: In parallel, total capacitance is the sum of individual capacitances (Cp = C1 + C2), which increases the total. In series, the reciprocal of the total capacitance is the sum of the reciprocals (1/Cs = 1/C1 + 1/C2), which decreases the total.
- Voltage: In parallel, voltage is the same across all capacitors. In series, the total voltage is divided among the capacitors.
- Charge: In parallel, the total charge is divided among the capacitors. In series, the charge is the same on all capacitors.
6. How does adding another capacitor in parallel affect the total energy stored by the circuit?
Adding another capacitor in parallel will increase the total energy stored by the circuit, assuming the voltage source remains constant. This is because adding a capacitor increases the equivalent capacitance (Cp). According to the energy storage formula, U = ½CpV², since Cp increases and V remains the same, the total stored potential energy (U) must also increase.
7. Can you give a practical example of where capacitors are used in parallel?
A common real-world application is in power supply filter circuits. After converting AC to DC, the resulting voltage often has ripples or fluctuations. Multiple capacitors are connected in parallel across the DC output to smooth out these ripples. Their combined large capacitance acts as an energy reservoir, supplying current when the voltage drops and absorbing excess charge when it rises, resulting in a more stable DC voltage.
8. What are the safety risks associated with high-power capacitor banks connected in parallel?
In high-power applications, parallel capacitor banks can be dangerous because they store a very large amount of energy at the same voltage. The main risks are:
- Rapid Discharge: An accidental short circuit can cause an extremely rapid and high-current discharge, leading to explosive failure, equipment damage, or severe electrical shock.
- Cascading Failure: If one capacitor in the parallel bank fails (by shorting), the other capacitors will discharge through it, potentially causing a chain reaction that destroys the entire bank.
