1 Electric Current
Current and charge
Electric current is the flow of charged particles, usually electrons, around a circuit. Metals are good conductors
of electricity because they have free electrons that can move around easily.
Current is measured in amperes, or amps.
Charged particles have a charge which is either positive or negative. The strength of a charge can be found
using the formula:
We can use this formula to define the coulomb:
One coulomb is the amount of charge which flows past a point when a current of 1 ampere flows for
1 second
Electron flow
When you attach a battery to a small bulb with wires, you would say that the current is flowing from the
positive terminal of the battery to the negative one. This is called conventional current. The electrons,
however, flow from the negative terminal to the positive. This electron flow is in the opposite direction to the
conventional current, and care must be taken to not confuse the two. When we just say current it is assumed
that we are talking about conventional current.
The reason for this is that the direction of conventional current was chosen before people knew what was
happening inside a conductor when a current flows.
Resistance
Any component with electrical resistance opposes the flow of an electrical current.
Electrical resistance
In an electrical circuit, current flows around it. Each component in the circuit has a resistance, which resists the
flow of the current.
The voltage that you get from the power supply can be simply described as the "push" given to the electrons
to go around the circuit.
It would then make sense to say that the greater the voltage, the greater the current, and the greater the
resistance, the lower the current. The current flowing around the circuit could then be written as the equation:
.
For example, if you were to connect a 9 volt power supply to a 3 Ω (read as 3 ohm) resistor, you could use the
formula above to find the current.
, so I = 3A.
A particular arrangement of this formula is used to define resistance and the ohm.
.
This says that the resistance of a component is the voltage across it for every unit of current flowing through it.
More formally this can be written as:
The resistance of a component in a circuit is the ratio of the voltage across that component to the current in it.
The unit of resistance, the ohm (Ω), is defined so that one ohm is the resistance of a component that has a
voltage of 1 volt across it for every amp of current flowing through it. In other words, one ohm is one volt per
amp.
Ohm's law
In many components, the voltage across it is proportional to the current flowing through it. You can make this
observation on a circuit with a resistor of a known resistance, a voltmeter, an ammeter, and a power supply
with a variable voltage. As you increase the voltage, the current will also increase. You will come to the
conclusion that, with the constant of proportionality equal to R. This gives us V = IR, an arrangement of the
familiar formula.
Components where V I, are known as ohmic conductors, and have a constant resistance. They are said to
follow Ohm's law, which states that:
“For a conductor at constant temperature, the current in the conductor is proportional to the voltage across
it.”
Note that not all components are ohmic conductors, and can have varying values of resistance. You will have
to use the formula
to find the resistance for specific values of V and I.
Below you can see 3 graphs with current on the vertical axis, and voltage on the horizontal axis. Where the
graph is a straight line, the voltage is proportional to the current. Therefore only the metallic conductor is an
ohmic conductor.
A diode and a filament lamp are two examples of non-ohmic conductors. The diode is designed to only allow
current through in one direction, hence the use of negative values on its graph. The filament lamp doesn't
have a constant temperature, which according to Ohm's law is required for a component to be an ohmic
conductor. Instead, it heats up as a current passes through it, which has an effect on the resistance.
Resistivity
The resistivity of a material is the property that determines its resistance for a unit length and unit cross
sectional area of that material. Copper, for example, is a better conductor than lead, and so lead has a higher
resistivity than copper. You can compare different materials in this way.
Resistivity, ρ (rho), is defined by the equation:
Where ρ is resistivity, R is the resistance, A is the cross sectional area of the material, and l is
the length of the material.
The units of resistivity are Ohm-meters, Ωm.
If we rearrange the above equation so that:
You can see that as the length of a wire is increased, its resistance will increase, and as the cross
sectional area of a wire is increased, its resistance will decrease. This is true provided that the
temperature is constant, and that the same materials are always used, to make sure that the
resistivity stays the same.
Voltage and energy
Earlier, we simply said that a voltage is the "push" given to electrons, or units of charge. Now, we will take a
look at voltage in terms of energy, and find a more accurate definition of the volt.
Potential difference
When you attach a voltmeter across a component, the voltage you are measuring is a potential difference
(p.d.). Electrical energy is being used up by the component, and so we can say that a potential difference is a
voltage where the charge is losing energy. Potential difference has the symbol V.
Potential difference is the energy lost per unit charge, and can be written as the following formula:
Electromotive force
A battery provides a certain voltage to the circuit, and the electrons are gaining energy from the battery as
they flow past. This voltage where the charge gains energy is called an electromotive force (e.m.f.), and has
the symbol V.
E.m.f. is the energy gained per unit charge, and can be written as the following formula:
Both the p.d. and e.m.f. are measured in volts, and one volt is equivalent to one joule per coulomb.
Electrical energy and power
Power is the rate at which energy is transferred, written as the formula:
To find a formula for electrical power, we take the following formula for voltage and make W the subject:
W  QV
Then we need to divide both sides by t to get power:
Recall that charge divided by time is current, we now have:
From the formula above, you can see that the electrical power is simply: the product
of current and voltage.
You can combine this with V = IR to give a further equation:
One last formula is for energy and is derived from the formula
power:
Therefore:
for
P  I 2R
2 D.C Circuits
Circuit diagrams
Here are the symbols and names for all of the components that you are required to know:
Series circuits
When resistors are set up in series, the formula to work out the total resistance is:
R = r1 + r2+.... + r (n-1) + rn
Where r is the individual resistance if a resistor in series.
Parallel circuits
When resistors are set up in parallel, the formula to work out the total resistance is:
Where r is the resistance of an individual resistor in parallel.
Internal resistance
All sources of electrical power have internal resistance, we represent this as small resistor, r contained within
the cell:
Thus,
Rtotal = Rn + r
Potential dividers
A potential (or voltage) divider is made up of two resistors. The output voltage from a potential divider will be
a proportion of the input voltage and is determined by the resistor values.
Kirchhoff's laws
1st Law states "The sum of the currents (A) entering a junction is equal to the sum of the current (A) leaving
the junction". This is a consequence of conservation of charge.
2nd law states that the e.m.f is equal to the voltage of the circuit. This is a consequence of conservation of
energy.
Use of other components
Thermistors can be placed in circuits when temperature plays a role. As the temperature increases, the
resistance of the device increases. This does not obey the Ohms law. Light dependent resistors are resistors
which decrease in resistance when exposed to light.
3 Electro-Magnetism
Fleming's left hand rule
Use your thumb, first and second fingers to point at 90° to each other: like the corner of a box.
First finger: Field
seCond finger: Current
THumb: THrust, thuMb: Motion
Formula
F is the force produced, measured in Newtons. I is current that the magnetic field is acting on, measured in
Amps. L is the length of the electrical wire.
4 Quantum Physics
Does light behave as a wave or as particles?
Interference experiments, such as Young's Slits, see below, can only be explained if we assume light is a wave.
The photoelectric effect can only be explained if light is a particle.
So what is light, particle or wave?
Don't like this? Get used to it, accept it, it is the current state of our knowledge.
Young's slits
Young's slit is all to do with interference patterns. Interference patterns are a feature of waves. Electrons are
particles, you will have been led to believe, but can be observed to have interference patterns. To get an
interference pattern, you must have a wavelength. This gives more evidence of Wave-particle duality.
The Photoelectric effect
In analysing the photoelectric effect quantitatively using Einstein's method, the following equivalent equations
are used:
Energy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron
Algebraically:
Where:
h
f
is Planck's constant,
is the frequency of the incident photon,
is the work function, or minimum energy required to remove an electron from atomic
binding,
is the maximum kinetic energy of ejected electrons,
f0
is the threshold frequency for the photoelectric effect to occur,
m
is the rest mass of the ejected electron, and
vm
is the velocity of the ejected electron.
Note: If the photon's energy (hf) is not greater than the work function (φ), no electron will be emitted. The
work function is sometimes denoted W.
Planck constant
The physicist Max Planck studied a phenomenon known as black-body radiation, and found that the
transmission of light was best treated as packets of energy called photons. The energy of a photon, E, is given
by the following formula:
Where E is the energy of the photon, h is the Planck constant
light.
, and f is the frequency of the
The Photon model
Over the ages, scientists have argued what light actually was. Newton argued that light is composed of
particles called corpussles and theorised that diffraction was due to the particles speeding up as they entered
a denser medium, being attracted by gravity. However he has since been proved wrong, now we can measure
the speed of light and have proved it to slow down in a denser medium. Albert Einstein thought that light were
discrete packets of energy which he called quanta.
Wave-particle duality
In 1924, Louis-Victor de Broglie formulated the de Broglie hypothesis, claiming that all matter has a wave-like
nature; he related wavelength, λ (lambda), and momentum, p:
This is a generalization of Einstein's equation above since the momentum of a photon is given by p = E / c
where c is the speed of light in vacuum, and λ = c / ν.
De Broglie's formula was confirmed three years later for electrons (which have a rest-mass) with the
observation of electron diffraction in two independent experiments. At the University of Aberdeen, George
Paget Thomson passed a beam of electrons through a thin metal film and observed the predicted interference
patterns. At Bell Labs Clinton Joseph Davisson and Lester Halbert Germer guided their beam through a
crystalline grid.
5 Electro-Magnetic Waves
Structure
Electromagnetic (EM) waves are transverse waves that carry energy. This means the light can be polarised like
all other transverse waves. Depending on the amount of energy, the waves create the Electromagnetic
Spectrum, comprising (from longest to shortest wavelengths) Radio, Microwave, Infrared, Visible Light,
Ultraviolet, X-ray, Gamma ray. Commonly referred to as EM "Radiation," these waves have wavelengths
ranging from several thousand kilometers (
m) to sub-picometers (
m).
The wave actually made up of two components which are perpendicular to the direction of the wave.
EM radiation can be thought of as particles (the photon) or as waves, which is commonly referred to as the
"Wave-particle duality".
The Speed of Light
All electromagnetic waves travel at the same speed (in a vacuum), and that is the universal constant known as
the "Speed of Light," most often abbreviated by the lower-case letter "c."
The speed of light is (exactly):
c = 299 792 458 m / s or
c = 983 571 056 ft / s
The Electro-Magnetic Spectrum
Type
Production
Uses
Dangers
Wavelength
(m)
Frequency
(Hz)
Gamma rays
Chemotherapy
Causes cancer by
damaging cells
Causes cancer by
damaging cells
x10-12
x10 20
x10-10
x10 18
Ultraviolet
Emitted during
radioactive decay
Produced by firing
electrons at a metal
target
Emitted by the Sun
Can cause skin
cancer
x10-8
x10 15
Visible light
Emitted by the Sun
7 x10-7 to 4x10-7
x10 14
Infra-Red
Emitted by hot
objects
Conventional cooking
Intense light can
damage sight
Can burn
x10-5
x10 12
Micro-waves
Produced by changing
currents in a
conductor
Microwave cooking
and communications
Can burn
x10-3 to x10-2
x10 10
Radio-waves
Produced by changing
currents in a
conductor
Communication and
media
Currently not
considered to be
hazardous
x1
x10 8 to x1010
X-rays
Medicine for looking at
bones
induces the
production of
vitamin D in the
skin
Useful Equations
To find out the energy of a particular EM wave or its frequency, one can use the several forms of the Einstein
Equation.
First, to determine an EM wave frequency, ν from its wavelength, λ. The wavelength multiplied by the
frequency is always a constant value: the speed of light, c. Hence,
c = fλ
so you can find the frequency from the wavelength, or vice versa from simply manipulating this relationship.
Next, to determine the energy from a smallest quantity of EM wave (photon). Here, we must introduce
another universal quantity known as "Planck's Constant," most commonly abbreviated by a lower-case "h."
Planck's constant is
h = 6.626068 x 10-34 m2kgs-1.
With this in place we can use the "Planck Equation," which provides a relationship between the frequency, f
and energy E of photon. The relation is as follows:
E = h f.
Now, if we only have the wavelength with which to start, we can manipulate Equation (1) to get what we
need.
c = fλ,
f = λ / c,
E = h c / λ.