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Why Coaxial Cables Are More Useful Than Twisted Pair Cables, And Theory Behind Them

Coaxial and twisted pair cables are two types of cables, which mainly differ in construction. Coaxial cables are by which we receive our cable TV network. Coaxial cable consists of a copper or aluminum wire which is surrounded by any insulator having large di-electric constant, over which wrapped around is a conductive layer. 

In twisted pair cables two insulated copper wires are twisted together like a DNA model. This is done to reduce the interference produced between the two cables.

In digital electronic communication, data is transferred in bits. Bits are electrical pulses carrying certian voltages. In typical communications millions of bits meaning millions of voltage pulses are sent and received in one second. As data is transferred in bits that is one and zeros, where one represents any particular higher voltage level while zero represents any lower voltage level, below the noise region. So in cable carrying these rapid voltage fluctuations, Rapid current fluctuations are produced. As we know that magnetic field is associated with current. And moreover changing current produces changing magnetic field. This changing current thus produces electro-magnetic waves.
Now think of a wire carrying millions of bits meaning millions of voltage and current fluctuations. This will in turn produce electro-magnetic waves coming out of the cable, having same frequency. These electromagnetic waves may be picked over by the other wire. This is known as interference and more technically, cross-talk. This is highly unwanted in communications because this type of propagation of signal distorts the signal present on the other wire.
In coaxial cable the di-electric constant of the material between the inner and outer cable is very high. As a result cross-talk becomes limited. That is why coaxial cables carry signal over a longer range when compared to twisted pair cables. In common twisted pair cables, repeaters are deployed after about every 100 meters distance.
Moreover data carrying capacity of twisted pair cables is also very less, when compared to coaxial cables. The data transmission capacity of twisted-pair cables typically ranges form 2 million bits per second to 100 million bits per second. Where as, capacity of coaxial cable normally ranges from 200 million bits to 500 million bits per second.
The material, with which the any particular cable is made up of, also matters a lot. As we know that every conductor has its inductance. Like wise, the transmission cables also have some inductance no matter very small due to smaller dimensions.
But when the signal is of very high frequency then according to Faraday's law, back EMF produced also becomes high due to direct relation.
                                Back EMF = L x di / dt
L = Self Inductance
i = Current
t = Time
At extreme high frequencies this back EMF becomes so much considerable that even the small amount of inductance in the numerator does not matters a lot. This considerable amount of back emf produced results in the limitation of the bandwidth. Because this back EMF produced is in the direction opposite to the signals propagation, as a result it tends to nullify the signal voltage. So signal becomes weak. So it loses its strength after covering a short distance, as there are resistance effects too. In twisted pair cables this factor is much evident, when compared to coaxial cables. So they cannot carry data over long range.
Greater the data carrying capacity of the medium is more band width it can support. That is why coaxial cables are mainly used for video/audio transmission services, like in TV cable transmission, while twisted pair cables are mainly used for audio data transmission only. For example, in telephone lines etc.