(a) Draw a labelled diagram of a step-up transformer. Obtain the ratio of secondary to primary voltage in terms of number of turns and currents in the two coils.
(b) A power transmission line feeds input power at 2200 V to a step-down transformer with its primary windings having `3000` turns. Find the number of turns in the secondary to get the power output at `220 V`.

Explanation

`V_(p) = -N_(p) (dphi)/(dt)` and `V_(s)= -N_(s)(dphi)/(dt)`
`N_(p')N_(s)` are the no. of term of turn in primary and secondary coils respectively.
`:. (V_(s))/(V_(p)) = (N_(s))/(N_(p)) = " turn s ratio"`
In step-up transformer
`N_(s) gt N_(p)`
So, `V_(s)gt V_(p)`
In step-down transformer
`N_(s) lt N_(p)`
So, `V_(s) lt V_(p)`
As energy is conserved the rate at which source transforms energy to the primary = rate at which primary transfers energy to secondary.

`I_(p)E_(p) = I_(s)E_(s) rArr (E_(s))/(E_(p)) = (I_(p))/(I_(s))`
For a step-up transformer,
`:.` From faraday's law of Induction, induced emf/turn is same for both primary and secondary coil.
Also, `E_(s) = E_(p')`
So, `E_("turn") = (dphi_(B))/(dt)= (E_(p))/(n_(p)) = (I_(s))/(I_(s))`
`rArr E_(s) = E_(p)(n_(s))/(n_(p))`.
Here, `n_(s) = ?, n_(p) = 3000 , E_(p) = 2200 V, E_(s) = 220 V`
`(E_(p))/(E_(s)) = (n_(p))/(n_(s))`
`2200/220 = (3000)/(n_(s))`
`n_(s) = (3000)/(10)`
`n_(s) = 300` turns.