Capacitors and capacitance

In a nutshell

Capacitors are electrical devices which are used to store electrical charge. They consist of two parallel plates of conducting material. The plates are separated by a dielectric which is an electrical insulator and prevents the charge from flowing between the plates.

Equations

Description	Equation
Capacitance	$C=\frac QV$
Capacitors in series	$\frac 1{C_{Total}}=\frac 1{C_{1}}+\frac 1{C_{2}}+\frac 1{C_{3}}+...$
Capacitors in parallel	$C_{Total}=C_1+C_2+C_3+...$

Variable definitions

Quantity Name	Symbol	Derived Unit	SI BASE Units
$capacitance$	$C$	$F$	$kg^{-1}\,m^{-2}\,s^4\,A^2$
$charge$	$Q$	$C$	$A\,s$
$potential \ difference$	$V$	$V$	$kg\,m^2\,s^{-3}\,A^{-1}$

Capacitors

Capacitors are electrical devices which can store electrical charge. Capacitors are made up of two parallel plates which are separated by a dielectric.

Note: A dielectric is an electrical insulator. It depends on the capacitor, it could be an air gap or it could be an insulating material.

Physics; Capacitance; KS5 Year 12; Capacitors and capacitance

1	Dielectic
2	Parallel conducting plates

The circuit symbol for a capacitor is two parallel lines.

Physics; Capacitance; KS5 Year 12; Capacitors and capacitance

When a capacitor is connected to a direct current power supply, positive and negative charges build up on each plate respectively. The dielectric prevents the charge crossing between the plates causing a potential difference across the plates.

The charged plates creates a uniform electric field between them.

Capacitance

The capacitance of a capacitor is defined as the charge per unit potential difference. The higher the capacitance, the more charge it is able to store per unit of potential difference across the plates.

This is given mathematically by:

$C=\frac QV$

Note: The unit of capacitance is the farad (F). The farad is a very large unit of capacitance, so it is very common to see the units of capacitance in $mF$ , $\mu F$ , $nF$ and even $pF$ .

Example

A $650 \, \mu F$ is connected to a $9.0 \, V$ battery. Calculate the charge stored across the capacitor.

Firstly, write down the known values:

$C=650 \, \mu F =650 \times 10^{-6} \, F \newline \\[0.1in]V=9.0 \, V$

Next, write down the equations needed and rearrange if necessary:

$C=\frac QV \rightarrow Q=CV$

Then, substitute the values into the equation:

$Q=650\times 10^{-6} \times 9 .0 \newline \\[0.1in]Q=5.85\times 10^{-3}$

Make sure to include units and round to the lowest number of significant figures of the values given by the question:

$charge \ stored, \ Q=5.9 \times 10^{-3} \, C$

The charge stored by the capacitor is $\underline{5.9 \times 10^{-3}}.$ 

Capacitors in series and parallel

If capacitors are placed in series, the potential difference across them will be shared amongst the number of capacitors.

If the capacitors are identical, then each capacitor will have an equal share of the potential difference. Each capacitor will store the same amount of charge.

Mathematically this can be shown as:

$\frac 1{C_{Total}}=\frac 1{C_{1}}+\frac 1{C_{2}}+\frac 1{C_{3}}+...$

If the capacitors are in parallel, then the potential difference across each capacitor will be the same. As the charge stored is directly proportional to the potential difference, each capacitor will be able to store the same amount of charge.

This means all of the capacitors in parallel would store the equivalent as one large capacitor with the sum of their individual capacitances.

Mathematically this can be shown as:

$C_{Total}=C_1+C_2+C_3+...$

Tip: Mathematically capacitors are the opposite to resistors. This might make it easier to remember for your exam!

Uses of capacitors

Capacitors are incredibly common in lots of different circuits and appliances. If you have ever seen a circuit board inside an appliance then there are normally a variety of cylindrical circuit components which are soldered onto the board.

These are capacitors and serve lots of different purposes depending on the appliance.

Note: It is incredibly dangerous to touch or mess with capacitors even after the power supply has been disconnected. This is because capacitors store the charge supplied and need to be safely discharged before handling else you could get a big shock!

Some common uses of capacitors are

Energy storage. Capacitors can act as temporary battery's but only temporary as they discharge very quickly.
Power conditioning. Capacitors can help smooth out current fluctuations particularly for AC rectification.
Computers. Capacitors provide smoothing of electrical signals.
Camera flashes. Batteries charge the capacitors which then discharge very quickly through a bulb creating a quick flash of light.