Sim's Electrical Companion
Sine Waves, Radians and Degrees
The sine wave used to describe alternating current needs some explanation. If you consider a rotary generator and show its position in relation to the sine it makes a lot more sense. The illustration starts at point 0,0 X,Y and as the generator travels anticlockwise through one cycle at 90 degrees it reaches the positive half cycle peak. At 180 degrees it starts the negative half cycle at this point the current direction reverses. at 270 degrees it reaches the negative half cycle peak. At 360 degrees the cycle is complete.
In the UK the frequency of alternating current is highly regulated and is maintained at 50 hertz. Most of the world is supplied by a frequency of either 50 or 60 hertz. The reason this is so finely controlled is because inconsistencies in frequency cause loses in power and in severe cases equipment failure. Mains frequency is also used for regulating electric and electronic clocks. Deviations in the supply frequency are corrected by short term corrections of +/- approximately 10mHz to get clocks back to the correct time. The wavelength of a complete cycle is usually denoted by the Greek letter lambda λ which is equal to velocity (m/s) / frequency (Hz).
The time period of each complete cycle is given by 1 / frequency:
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The time period for UK frequency is 1/50 = 0.02 seconds per cycle.
In some circumstances a localised frequency of 400 Hz is used for specialised equipment e.g. Motors, server farms and on mobile machines like aircraft and in shipping. One benefit of 400 Hz is the greatly reduced size and weight of transformers due to the increased changes in magnetic flux. The down side is long distance transmission creates huge loses in power due to inductive effects.
The graph above describes how a sine is generated as a two dimensional graphical representation of the rotation of a generator over time. I described the significant steps of that journey in degrees but for the purpose of electrical calculation it is far better described in radians. A radian is literally the radius of the circle that is being plotted. So within the circumference of a circle the path is 2π radians. The diagram below is to show the sine described in radians. This is fundamental in understanding alternating current especially when dealing with reactive elements that are dependant upon frequency like capacitance and inductance.
The 360 degrees in a circle is an historic number and is essentially arbitrary. It is thought that it may be based on the 360 day Persian calendar or it could simply be because of the use of base 60 number system (sexagesimal).
The system was widely used in commerce because 60 is highly divisible into whole numbers. 60 can be divided by 1,2,3,4,5,6,10,12,15,20 & 30 so before the advent of the calculator it was easier to work with.
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To convert degrees to radians it is worth remembering that 180 degrees is equal to 1π radians.
So 180/π = 57.296 degrees = 1 Radian
Frequency
Before the advent of the national grid power generation was not constrained to a particular voltage or frequency so in some cases electrical equipment designed for use in one region may not be compatible in another region. This has obvious drawbacks that were addressed in the design and construction of the national grid.
The SI unit for frequency was named after Heinrich Hertz as acknowledgement for his work proving Maxwell's theory of electromagnetic waves. Frequency is the amount of waves there are in one second so the time period of a whole cycle is simply calculated:
Electromagnetic waves manifest themselves in many differing ways and their effects are extremely varied depending upon their frequency and wavelength.
Gamma Rays
Symbol γ The shortest wavelength in the spectrum and the highest energy. Gamma rays are photons that have been emitted from the radioactive decay of atomic nuclei. Gamma radiation is highly penetrating and ionising. Even small amounts of exposure can cause severe damage to living cells.
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X Rays
Wavelengths of 0.01 - 10nm at 3x10^19 - 3x10^19 Hz. Gamma rays and x-rays are only distinguished by the manner in which they were produced. Where Gamma rays are emitted from the nuclei, X-rays are a result of electron interactions producing high intensity photons. The X is a historic acknowledgement that they were proved to exist but were not understood. X-ray photography is a technique of aiming a controlled burst through materials to determine their density. They travel through skin and soft tissue but not so much through bone.
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Ultraviolet
At 10 - 400nm humans cannot see ultraviolet light (UV) but we can see the effects of it. Commonly called black-light it causes some objects to fluoresce like white T-shirts, teeth & phosphor coatings on fluorescent tubes. It is not energetic enough to cause ionisation but it can cause chemical reactions. Sun light is approximately 10% UV light and forms vitamin D in most mammals. The downside is it can also cause burns through prolonged exposure hence our use of sun cream which blocks ultraviolet radiation.
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Visible Light
The only light we can detect with our eyes is in fact a very narrow band of the electromagnetic spectrum. Ranging from Purple 400nm to red 700nm and the range is all combined to create white light.
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Infra Red
Forms more than half of the radiation from the sun it is well known for its heating effects. Infra red was discovered by its effect on a thermometer when a prism was used to split white light. Can be seen by some specialised animals for example Boas, Pythons and Vipers have a heat sensing pit organ.
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Radio Waves
Wavelengths of 1mm at 300GHz to 10,000km at 30Hz. Radio waves include microwaves and are largely used for communication systems. Radio-waves are non ionising although they can cause heating effects e.g. microwaves above 300Mhz.
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Microwaves have frequencies of 300MHz-300GHz with wave lengths between 0.1 and 1m. Used in high data transmission for point to point communications. Also they are used for heating food although technically a misnomer they are not micro in size.