The capacitance, $C$ of a capacitor is the charge stored per unit potential difference. It is simply the ratio of the charge stored to the voltage applied the ends of the capacitor: $$ \begin{equation}\begin{aligned} C=\frac{Q}{V}\\ \end{aligned}\end{equation} $$
It is measured in Farads ($F$): $$ \begin{equation}\begin{aligned} \frac{Q}{V}\rightarrow \frac{\text{Coulombs}(C)}{\text{Volts}(V)}=CV^{-1}=F\\ \end{aligned}\end{equation} $$
Because a farad of capacitance is very large for most everyday applications, it is common to see capacitance being stated in microfarads ($\mu F$): $$1\mu F=1\times 10^{-6}F$$
Capacitors
A capacitor is a device that stores charge and it consists of two sections (sheets or plates) of conducting material, placed close enough to have a significant electric field exist between them but not too close as to cause the charge to jump from one side to the other.
A dielectric is the insulator that separates the two sections of conducting material and prevents charge from moving from one plate to the other.
Without an electric field between the plates, there can be no storage of equal and opposite charge on the plates of the capacitor.
The capacitance can be expressed in terms of the factors affecting it: $$ \begin{equation}\begin{aligned} C=\frac{\epsilon A}{d}\\ \end{aligned}\end{equation} $$ where $\epsilon$ is the permittivity of the material, $A$ is the cross-sectional area and $d$ is the separation distance of the plates.
1) What is the SI units of $\epsilon$?
- $F$
- $Fm^{-1}$
- $Fm^{-2}$
- $Fm$
Dielectric polarization
When the electric field is applied to the dielectric, the particles of the dieletric become polarized - a net positive charge on the side facing the capacitor’s negative plate and a net negative charge facing the positive plate.
This creates an internal electric field which serves to weaken the electric field between the plates. The capacitance increases because the weakened electric field allows the capacitor to store more charge for the same applied voltage.
Uses of capacitors
Some ways that we use capacitors in electrical circuits are:
- Acting as temporary batteries
- Smoothing the output of full-wave rectifiers
- Creating high-pass, low-pass and band-pass filters
- Filtering fluctuations in current