A long and thin wire has more resistance than a short and thick one. A simple analogy is a road - the more lanes there are, the more cars can go through. The resistance of a wire with a constant width, therefore, can be calculated as:
where formula_6 is the length of the conductor, measured in meters [m], formula_7 is the cross-sectional area of the conductor measured in square meters [m²], and (Greek: rho) is the electrical resistivity (also called "specific electrical resistance") of the material, measured in ohm-meters (Ω m).
Example:
Calculate the resistance of copper wire with a radius of 2mm and a length of 5 meters.
Solution:
Because: formula_5
formula_15
Resistors are used in electrical circuits to provide electrical resistance.
Electromagnetic induction
Electromagnetic induction is where a voltage or current is produced in a conductor by a changing magnetic flux. It may happen when a magnet is moved in a solenoid, thus changing the magnetic flux.
When a coiled wire is introduced near a magnet, the magnetic lines of force pass through the coil. This causes the magnetic flux to change.
Magnetic flux is represented by the symbol formula_1, therefore we can say that formula_1 = BAcos(a) and the resulting unit will be formula_3, where T is the unit for magnetic field and formula_4 is the unit for area.
The changing magnetic flux generates an electromotive force (EMF). This force moves free electrons in a certain way, which constitute a current.
Michael Faraday found that an electromotive force is generated when there is a change in magnetic flux in a conductor.
His laws state that:
formula_5
where,
formula_6 is the electromotive force, measured in volts;
formula_7 is the change in magnetic flux, measured in webers;
formula_8 is the change in time, measured in seconds.
In the case of a solenoid:
formula_9
where,
N is the number of loops in the solenoid.
The negative sign in both equation above is a result of Lenz's law, named after Heinrich Lenz. His law states that the electromotive force (EMF) produces a current that opposes the motion of the changing magnetic flux.
BBC Proms
The Proms are concerts which are part of a big music festival. “Proms” is short for “Promenade Concerts”. The Proms are organized by the BBC, so they are called the “BBC Proms”. They take place in the Royal Albert Hall, in London from mid-July to mid-September every year.
The Proms started more than 100 years ago, in 1895. Concerts were expensive in those days, and not many people had enough money to go and hear good music. Most people were only able to hear good music when they went for walks in the London parks where there were Promenade concerts. Orchestras and bands played in bandstands. Most of the music was popular and easy to listen to. People could enjoy the music while they walked about.
In the centre of London there was a building called the Queen's Hall. A man called Robert Newman organized concerts there. He had an idea. He wanted to start a series of concerts which ordinary people (people who were not rich) could afford to go to. He wanted to start a series of “promenade concerts” (in French “se promener” means “to walk”). The idea was that people could have standing places which would not cost much money. There would also be seats for people who could afford to pay more.
Robert Newman knew a very good young conductor, Henry Wood. He asked him to be the conductor of the Proms. A man called Dr Cathcart gave them enough money to get an orchestra together. On 10 August 1895 the first Promenade Concert took place in the Queen’s Hall. The price of a promenade ticket (a ticket for a standing place) was one shilling.
The Promenade Concerts were a big success, and soon became known as the "Henry Wood Promenade Concerts". Wood conducted both popular music and the classical works of Mozart, Beethoven, Mendelssohn, Tchaikovsky, Brahms and Wagner, as well as some English composers. Wallace and Cowan, popular then, have today faded from the scene, although Elgar and Delius have survived due to Wood's Proms. This broke the convention that famous composers, conductors and singers could not be English.
Some of the music Wood conducted was very new indeed. In 1912 he conducted a piece called “Five Orchestral Pieces” by an Austrian composer Arnold Schoenberg (1874-1951). Its initial lack of appreciation was overcome by inviting Schoenberg to come to England and conduct it himself in 1914.
Henry Wood conducted almost all of the Proms for fifty years, until just before his death in 1944. His innovations with the orchestra staff were to abolish deputies (allegedly in 1904 when, at one rehearsal, none of the regular orchestra, and only deputies attended). Forty members of the orchestra were offended by that decision, and broke away to form what is now the London Symphony Orchestra. In 1913, Wood was also the first English conductor to appoint women to play in his orchestra.
In 1927 the BBC started to fund Proms. The radio was a new invention (then termed the “wireless”). Radio broadcasts increased interest in attending live concerts. In 1930 the BBC Symphony Orchestra was formed, playing at a majority of Prom concerts.
In 1941, during World War II, the Queen’s Hall was destroyed by bombs. The Proms continued to take place in the Royal Albert Hall. Then it became too dangerous in London and the Proms were held in Bristol and then Bedford. After the War the Proms went back to the Royal Albert Hall. They have been held there ever since. From the 1940s to the late 1960s the BBC Symphony Orchestra played at most of the concerts under the very popular conductor Sir Malcolm Sargent whose Last Night speeches became legendary for their wit.
Today the Proms are very different from when they started. It is much more international. The BBC Symphony Orchestra play several concerts each season but there are lots of other orchestras from all over the world who come to play. People can hear different kinds of music at the Proms: not just classical music but jazz and music from far-away countries. In 2005 the famous Indian musician Ravi Shankar played the sitar at one of the Proms. In 2008 the violinist Nigel Kennedy played the "Violin Concerto" by Edward Elgar with the BBC Concert Orchestra, then came back an hour later to give a Late Night Prom of jazz music with the Nigel Kennedy Quintet.
The Proms also include special activities for children. The television programme Blue Peter put on a Blue Peter Prom which is given twice during the weekend at the beginning of the school holidays in late July. In the 2007 season they organized a special Brass Day where children could take part with their instruments. BBC Music Intro put on workshops in the late afternoon for children and their families to learn about music. In 2008 there was a Dr Who prom which was extremely popular, especially with children. This theme will be repeated in 2010.
Henry Wood encouraged composers to write new music by performing it at the Proms. Today this tradition continues as the BBC often commission composers to write new music for the Proms. Some pieces which had their first performance at the Proms have become very well-known, e.g. "The Confession of Isobel Gowdie" by James MacMillan (first performed in 1990), or John Tavener's "The Protecting Veil" (first performed in 1989).
For many years now every Prom has been broadcast live on BBC Radio 3. Some of them are shown on television, either on BBC2 or on BBC4 where viewers can, if they wish, read comments about the music as it is played. People can also listen to the Proms for several days afterwards on the Proms website.