Capacitors are short term chargestores, a bit like an electrical spring. They store energy in the form of an electric field. A battery stores energy as chemical energy, released when the chemical reaction proceeds. They are used widely in electronic circuits. At its simplest the capacitor consists of two metal plates separated by a layer of insulating material called a dielectric.
The picture shows some different capacitors:
The two components on the right are electrolytic capacitors. The others are nonelectrolytic capacitors.
The symbol for a capacitor is shown below:
There
are two types of capacitor, electrolytic
and nonelectrolytic.
We won’t worry at the moment what these terms mean, other than to say:
Electrolytic
capacitors hold much more charge;
Electrolytic
capacitors have to be connected with the correct polarity, otherwise they
can explode.
If
we pump electrons onto the negative plate, electrons are repelled from the
negative plate. Since positives do
not move, a positive charge is induced. The
higher the potential difference, the more charge is crowded onto the negative
plate and the more electrons repelled from the positive plate.
Therefore charge is stored. The
plates have a certain capacitance.
Capacitance depends on:
Area;
Separation of the plates;
Dielectric.
In a capacitor, an electric field is formed.
If the electric field is too strong, the dielectric will break down and a spark
will jump. The maximum voltage is known as the working voltage.
Capacitance
Capacitance
is
defined as:
The
charge required to cause unit potential difference in a conductor.
Capacitance
is measured in units called farads
(F) of which the definition is:
1
Farad is the capacitance of a conductor, which has potential difference of 1
volt when it carries a charge of 1 coulomb.
So
we can write from this definition:
Capacitance
(F) = Charge (C)
Voltage (V)
In
code, this is written:
[Q  charge in coulombs (C);
C – capacitance in farads (F);
V
 potential difference in volts (V)]
A
1 farad capacitor is actually a very big capacitor indeed so instead we use microfarads
(mF)
where 1
mF = 1 ×
10^{6} F. Smaller
capacitors are measured in nanofarads (nF),
1 × 10^{9 }F, or picofarads (pF), 1
×
10^{12} F. A
working
voltage is also given.
If the capacitor exceeds this voltage, the insulating layer will break
down and the component shorts out. The
working voltage can be as low as 16 volts, or as high as 1000 V.
Write down what is meant by the following terms:

Voltage and Charge
The relationship between voltage and charge is one of direct proportionality:
The gradient of this graph gives the capacitance.
You can verify this for yourself by charging up the capacitor. You use a voltmeter to measure the voltage, and a chargemeter which measures the charge. The picture shows one:
The voltage rises as we charge up a capacitor, and falls as the capacitor discharges. The current falls from a high value as the capacitor charges up, and falls as it discharges.
If
we connect a capacitor in series with a bulb:
If
connected to a d.c. circuit, the bulb flashes, then goes out.
In
an a.c. circuit, the bulb remains on.
We can say that a capacitor blocks d.c., but allows a.c. to flow.
The behaviour of capacitors with AC circuits is discussed in Electricity Tutorial 11.
For information on how capacitors are used in Electronics, you can visit the electronics pages of my sister website HERE.
The capacitor does NOT conduct electricity. The "flow" of a.c. is due to the charge and discharge of the capacitor. 
Why does a capacitor appear to allow ac to flow, but not dc? 

What is the charge held by a 470 microfarad capacitor charged to a p.d. of 8.5 V? 
Measuring Capacitance
This circuit can be used to measure the value of a capacitor:
The
reed switch is operated from a 400 Hz supply.
It
operates on the forward half cycle, to charge up the capacitor.
No
current flows on the reverse half cycle so the reed switch flies back to
discharge the capacitor.
We can use:
to work out the charge going onto the plates. We also know that:
so we can combine the two relationships to give:
Therefore:
Since:
we can now write:
This is an experiment that you may well do in class, although details are not expected for the exam.
Why does the circuit only operate on the forward halfcycle? 

A capacitor is connected to a 12volt power supply by a reed switch operating at 400 Hz. The ammeter reads 45 mA. What is the capacitance of the capacitor? 
When we charge up a capacitor, we make a certain amount of charge move through a certain voltage. We are doing a job of work on the charge to build up the electric field in the capacitor. Thus we can get the capacitor to do a job of useful work.
We know that:
1.
Energy = charge × voltage
2. Q = CV
This second relationship tells us that the charge – voltage graph is a straight line:
The
capacitor is charged with charge
Q to a
voltage
V.
Suppose we discharged the capacitor by a tiny amount of charge,
dQ.
The resulting tiny energy loss (dW)
can be worked out from the first equation:
dW = V × dQ
This is the same as the area of the pink rectangle on the graph.
If
we discharge the capacitor completely, we can see that:
Energy
loss = area of all the little rectangles
=
area of triangle below the graph
By substitution of
Q
= CV, we can go on to write:
or:
What is the energy held by a 50 000 mF capacitor charged to 12.0 V? 
Using Calculus to work out the Energy
We have seen a graphical method to work out the energy.
The
capacitor is charged with charge
Q to a
voltage
V.
Suppose we discharged the capacitor by a tiny amount of charge,
dQ.
The resulting tiny energy loss (dW)
can be worked out from the first equation:
dW = V × dQ
In calculus notation we can write, using Q as the integrand (term to be integrated):
Since Q = CV, we can rewrite this and use the power rule of integration to write:
When this job of work is done, the amount of energy transferred is E. Therefore:
We can also use V as the integrand:
Since V = Q/C, we can write:
When this job of work is done, the amount of energy transferred is E. Therefore:
Maths Note Differentiation Differentiation is about determining the gradient of a graph.
There are a number of rules of differentiation We will use only two here.
Let us suppose we have a a straight line graph that follows the general relationship:
y = mx + c If we want to differentiate this, we get:
Therefore:
This tells us that the gradient is m.
Maths Window Integration Integration is the reverse process of differentiation. The idea is shown in the picture below:
The 2x term is the function. The function to be integrated is sometimes called the integrand. Therefore we write this in calculus form as:
The dx term shows that the little strips go along the xaxis. The integration symbol is a fancy capital letter 'S', which means "summed together". So we now write:
The C term is a constant. When we differentiated, the constant that was added to the function had a differentiated value of 0. Now we are applying the process in reverse, we need to have a definite value for the constant.
Here are some rules for integration:
Often you will need to integrate between two points. You may see an equation like this:
This means you have to work out the value of the integral at p and the value of the integral at q, and then subtract one from the other. This is shown in the picture below. The constant, C = 0 for the sake of this argument. 