A home is supplied with electrical power at 220V from a transmission line operating at 4.4 k.V. The efficiency of the transformerin the locality is 95 %. The power generating station is 1km away from the transformer and the transmission line wire has a resistance of `50 Omega//km`. Find
(a) turns ratio of the tranformer.
(b) what current will be drawn from the transmission line when varous appliances in the home draw 10 A from the transformer ?

Explanation

Here,
Emf induced across primary coil,
`E_(p) = 4.4 KV`
`= 4.4 xx 10^(3) V`
Emf induced across secondary coil `E_(s) = 220 V`
(a) If `N_(p)` is turns I primary coil and `N_(s)` is tuurns in secondary coil, then
Turns ratio = `(N_(p))/(N_(s)) = (E_(p))/(E_(s)) = (4.4 xx 10^(3))/(220) = 20`
`= N_(p) : N_(s) = 20:1`
(b) `therefore` Efficiency `eta=(E_(s)I_(s))/(E_(p)I_(p))`
`I_(s) and I_(p)` are currents in secondary and primary coils respectively so,
`(95)/(100) = (220 xx 10)/(4.4 xx 10^(3) I_(p))`
`I_(p) = (220 xx 10 xx 100)/(4.4 xx 10^(3) xx 95)`
= 0.53 A