Learning objectives of the lecture
- Electrostatic fields strength, Electric flux density
- Capacitance
- Capacitors in parallel and series
- Energy
- Magnetic flux and flux density, permeability
- Inductance
- Inductors in series and parallel
A capacitor is an electrical device that is used to store electrical energy. Next to the resistor the capacitor is most commonly encountered component in encountered component in electrical circuits. They are used in time delay circuits and in in time delay circuits and in electrical filters and oscillators. The latter are also used in Magnetic Resonance Imaging (MRI) for transmitting and receiving radiofrequency signals.
Given by Coulomb’s law, the force of attraction or repulsion between two electrically charged bodies at distance d is given as follows :
Capacitance is the ability of a body to store electrical charge. The capacitance C is given by the following equation $ C=\frac{Q}{V} $
The SI units for capacitance is farads (F) or Coulomb per Volt as suggests the formula. Note that the charge Q is current times time (Q= I⋅t)
The electric flux $ \psi $ is proportional to the number of electric field lines going through a virtual surface. It is measured in Coulombs
For a charge of Q Coulombs, the flux is \psi = Q Coulombs. Now, the electric flux density is the amount of flux passing through an area A that is perpendicular to the direction of the flux. $ D=\frac{Q}{A} $ measured in C.m-2
It is the measure of resistance that is encountered when forming and electric field in a medium:
$ \varepsilon_0 $ is the permittivity of free space. When an insulating material (dielectric) such as paper, mica or ceramic is introduced into the electric field, the ratio is modified:
$ \frac{D}{E}=\varepsilon_0 \varepsilon_r $; where $ \varepsilon_r $ is the relative permittivity
It has no units and some typical values are listed below:
It is simply proportional to the area A of a plate and inversly proportional to the plates’ spacing d. Also depends on the dielectrics between the plates: n being the number of plates (a capacitor is at least made of 2 plates of course)
What needs to be remembered is that capacitors in parallel acts exactly like resistors in series: they just add up. Hence if the circuit for example has only three capacitors in parallel, the total capacitance is given as follow :
This of course works the opposite way : exactly like resistors in series. Hence if the circuit has for example three resistors is series, the total resistance is given as follow :
The energy stored by a capacitor is given by :
Chapter to be completed…