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In addition to the revision notes for Capacitance and Capacitors on this page, you can also access the following Electrostatics learning resources for Capacitance and Capacitors
Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
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14.7 | Capacitance and Capacitors |
In these revision notes for Capacitance and Capacitors, we cover the following key points:
By definition, the amount of charge a conductor can store when a potential difference is applied is known as capacitance.
From experiments, it is found that the amount of charge accumulated on the conductor increases with the increase in potential difference. Therefore, the capacitance C of a conductor is
The unit of capacitance (here Coulomb per Volt) is known as Farad [F].
A capacitor is a system composed by two conductors separated by a dielectric (usually air). Most capacitors however are of three designs:
Once the capacitor is charged, its two conducting parts carry equal but opposite charges. Therefore, we consider the charge of one plate only when calculating the capacitance of a capacitor.
A parallel plate capacitor consists of two identical parallel plates, each of them having an area A and separated by a distance d between them. The capacitance of parallel plate capacitors is
where ϵ is the relative permittivity of dielectric the capacitor is immersed in, ϵ0 is the electric constant, A is the area of one plate and d is the distance between the plates.
A cylindrical-shaped capacitor is a system composed by two coaxial cylinders. The parameters of a cylindrical capacitor are:
The capacitance of a cylindrical-shaped capacitor is
A spherical capacitor is a system composed by two concentric spheres of radius a (the smallest) and b (the largest). The capacitance of spherical capacitors is:
Capacitors have fixed values like most electric devices. This is because it is impossible to produce capacitors by demand. Therefore, we combine two or more capacitors to change their capacitance. The two main types of capacitors combination are:
The total capacitance of the series combination of a system composed by two capacitors is
We can extend the above rule for more than two capacitors as well, that is
As for parallel combination of capacitors, the total capacitance is
This formula is also true for a system composed more than two capacitors connected in parallel, that is
The source (here the battery) does some work to charge a capacitor from 0 to Q (i.e. increasing the charge of capacitor by ΔQ). This process makes the capacitor able to store electric energy in its plates in the form of potential energy. This potential energy is
The above equation into other forms as needed using the capacitor formula C = Q /ΔV. Thus, we can write
and
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