State the underlying principle of a transformer. How is the large-scale transmission of electric energy over long distances done with the use of transformers ?

Explanation

Principle : When an alternating voltage is applied to the primary, the resulting current produces an alternating magnetic flux which links the secondary and induces an emf in it. (mutual induction)
Derivation :
The induced emf or voltages `epsilon_(s)`, in the secondary, with `N_(s)` turns is
`epsilon_(0) = (-N_(s)d phi)/(dt)`
The alternating flux `varphi` also induces and emf called back emf, in the primary .This is
`epsilon_(p) = (-N_(p) d phi)/(dt)`
But `epsilon_(s) = V_(s) gt epsilon_(p) = V_(p)`
Therefore,
`V_(s) = (-N_(s)d phi)/(dt)` and `V_(p) = (-N_(p) d phi)/(dt)`
Hence `(V_(s))/(V_(p)) = (N_(s))/(N_(p))`
If the transformer is assumed to be 100% efficient (no energy losses), the power input is equal to the power output and scenes `P = VI rArr V_(p)I_(p) = V_(s)I_(s)`, then
`(V_(s))/(V_(p)) = (N_(s))/(N_(p)) = (I_(p))/(I_(s))`
The large scale transmission and distribution of electrical energy over long distances is done with the use of transformers the voltage output of the generator is stepped-up (so that the current is reduced and consequently, the `I^(2)R` loss is cut down). It is then transmitted over long distances to an area sub-station near the consumers there the voltage is stepped down. It is for the stepped down at distributing substations and utility poles before a power supply of 230 V reaches our homes.