Capacitance theory

Capacitance

 

Capacitance is the ability of a body to store charge in an electric field. Capacitance is also a measure of the amount of electric potential energy stored (or separated) for a given electric potential. A common form of energy storage device is a parallel-plate capacitor.

A capacitor, also called condenser, is a passive device capable of storing energy sustaining an electric field. It consists in a pair of conductive surfaces, typically in the form of sheets or plates, in a situation of total influence separated by a dielectric material or a vacuum.

If a voltage is applied to a capacitor, for example connecting it to an accumulator, it will be charged very quickly. A plate will acquire a negative charge and the other an equal amount of positive charge. For a given capacitor, the load acquired Q is proportional to the potential difference V.

The proportionality constant, C is called capacitor capacitance. Most of the capacitors have a capacitance between 1pF (pf = 10-12 F) and 1 µF (microfarad = 10-6 F).

The capacitance C is a constant for a given value and it depends on the structure of the capacitor.

 

Dielectrics:

In most capacitors there are an insulating sheet between the plates, called dielectric. It has several purposes. First, dielectrics are more resistant than air, so that they can be applied a higher voltage without load passes through the space between the plates. In addition, a dielectric allows that the plates get closer without touching, thus allowing greater capacitance. Finally, it has been experimentally found that if the dielectric fills the space between the two plates, the capacitance increases by a K factor, called dielectric constant.

 

Storage of electricity:
A charged capacitor stores electrical energy. This energy is equal to the work done to charge it. The net effect is to remove the charge in a capacitor charging a plate and add it to the other. This is what makes an accumulator when it is connected to a capacitor. A capacitor is not loaded instantly; it takes time. When is some charge on each plate, it is needed a job to add more burden of the same sign. The more load has on a plate, more work will be needed to add more.

The work required to add a small amount of charge, when there is a potential difference V between the plates is:

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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At first, when the capacitor is discharged, no work is needed to pass the first portion of charge. However, towards the end of the process, the work need to add one a load ∆q is much higher, as the voltage across the capacitor, which is proportional to the charge on the plates increase.

If the voltage across the capacitor is constant, the need to move the load Q would be:

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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But, since the voltage on a capacitor is proportional to the load that has accumulated, the voltage increases during its charges from zero to its final value. Thus, the work performed shall be equivalent to moving once all the Q load across a voltage equal to the average throughout the process. The average voltage is:

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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Therefore, we can say that the energy stored in a capacitor is:

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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FORMULA SUMMARY:

 

Capacitance:

(C = Capacitance in Farads; q = electric charge in Coulombs; V = voltage between the plates in Volts)

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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Capacitance of a charged conducting sphere:

(R = Radius)

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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Energy stored in a capacitor:

(W = work measured in joules)

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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Capacitance of a capacitor:

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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Plane capacitor:

(S = area of the plates; d = Separation between plates)

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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Spherical capacitor:

(R2 and R1 are the radiuses of the spheres exterior and interior)

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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Cylindrical capacitor:

(L = length)

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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Electrostatic Energy Density:

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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Capacitance for parallel plates capacitor:

bioprofe |exams with exercises about physics, chemistry and mathematics | Capacitance

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Being ε0 the permittivity of empty space: 8.85 · 10-12 C2 / N · m2.

 

 

 

 

You can download the App BioProfe READER to practice this theory with self-corrected exercises.

 

 

Books that we recommend to extend knowledge of the subject

2 Comments

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