[Physics Class Notes] on Capacitors in Parallel Pdf for Exam

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 = C_pV                   — (2)

 

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

 

C_pV = C₁V + C₂V + C₃V + C₄V 

C_pV = (C₁ + C₂ + C₃ + C₄) V

C_p = C₁ + C₂ + C₃ + C₄

C_p 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,

 

C_p = C₁ + C₂ + C₃

 

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

 

C_p = C₁ + C₂ + C₃ +………. +C_n

 

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,

 

C_p = 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 website and app.