Menu

Capacitance and Capacitors Revision Notes

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

[ 1 Votes ]

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

Electrostatics Learning Material
Tutorial IDTitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
14.7Capacitance and Capacitors


In these revision notes for Capacitance and Capacitors, we cover the following key points:

  • What is capacitance?
  • How to find the capacitance of a charged conductor?
  • What are capacitors?
  • How many types of capacitors are there?
  • How to find the capacitance of a specific capacitor based on its design?
  • Why the series and parallel combinations of capacitors are used in electrical circuits?
  • What are dielectrics and why do we insert them between the plates of a capacitor?
  • How to find the energy stored in a capacitor or system of capacitors?

Capacitance and Capacitors Revision Notes

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

C = Q/∆V

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:

  1. two parallel plates with some space between them,
  2. cylindrical capacitors, and
  3. concentric spheres

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

C = ϵ × ϵ0 × A/d

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:

  • Length, L
  • Radius of the smaller cylinder a, and
  • Radius of the smaller cylinder b.

The capacitance of a cylindrical-shaped capacitor is

C = 2π × ϵ × ϵ0 × L/ln a/b

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:

C = 4π × ϵ × ϵ0/1/a - 1/b

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:

  1. Series Combination of Capacitors. Two or more capacitors are connected in series if they are placed one after another in the same conducting wire of an electric circuit.
  2. Parallel Combination of Capacitors. If two or more capacitors are connected in two or more different branches of the same circuit, which have the same starting and ending point, we say they are connected in parallel.

The total capacitance of the series combination of a system composed by two capacitors is

1/Cs = 1/C1 + 1/C2

We can extend the above rule for more than two capacitors as well, that is

1/Cs = 1/C1 + 1/C2 + 1/C3 + ... + 1/Cn

As for parallel combination of capacitors, the total capacitance is

Cp = C1 + C2

This formula is also true for a system composed more than two capacitors connected in parallel, that is

Cp = C1 + C2 + ... + Cn

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

W = EPEC = Q × ∆V/2

The above equation into other forms as needed using the capacitor formula C = Q /ΔV. Thus, we can write

EPEC = C × ∆V2/2

and

EPEC = Q2/2C

Whats next?

Enjoy the "Capacitance and Capacitors" revision notes? People who liked the "Capacitance and Capacitors" revision notes found the following resources useful:

  1. Revision Notes Feedback. Helps other - Leave a rating for this revision notes (see below)
  2. Electrostatics Physics tutorial: Capacitance and Capacitors. Read the Capacitance and Capacitors physics tutorial and build your physics knowledge of Electrostatics
  3. Electrostatics Practice Questions: Capacitance and Capacitors. Test and improve your knowledge of Capacitance and Capacitors with example questins and answers
  4. Check your calculations for Electrostatics questions with our excellent Electrostatics calculators which contain full equations and calculations clearly displayed line by line. See the Electrostatics Calculators by iCalculator™ below.
  5. Continuing learning electrostatics - read our next physics tutorial: Electric Charges. Conductors and Insulators

Help others Learning Physics just like you

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

[ 1 Votes ]

We hope you found this Physics tutorial "Capacitance and Capacitors" useful. If you did it would be great if you could spare the time to rate this physics tutorial (simply click on the number of stars that match your assessment of this physics learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines.

Electrostatics Calculators by iCalculator™