(i) The primary of a transformer has 400 turns while the secondary has 2000 turns. If the power output from the secondary at 1100 V is 12.1 kW, calculate the primary voltage. (ii) If the resistance of the primary is `0.2 Omega` and that of the secondary is `2.0 Omega` and the efficiency of the transformer is `90 %`, calculate the heat losses in the primary and the secondary coils.

Explanation

i) Given, `N_(1) = 400, `N_(2)`=2000, `V_(2)=1100V
As `V_(1)=V_(2).N_(1)/N_(2)= 1100 xx 400/2000 = 220V`
ii) Resistance of primary, `R_(1) = 0.2Omega`
Resistance of secondary, `R_(2) = 2.0 Omega`
Output power =`V_(2)I_(2)`=12.1kW = 12100 W
`therefore` Current in the secondary, `I_(2)=P_(2)/V_(2) = 12100/1100 = 11A`
As, efficiency = ("output power")/("input power")
`rArr 90/100 = (12100W)/("input power")`
Input power, `P_(1) = (12100 x 100)/90 = 13.44 xx 10^(3)`W
Also, input power, `P_(1) = V_(1)I_(1)`
`therefore` Current in the primary,
`I_(1) = P_(1)/V_(1) = (13.44 xx 10^(2))/(220) = 61.1`A
Power loss in the primary,
`=I_(1)^(2)R_(1) = (61.1)^(2)xx 0.2 = 746.61`W
Power loss in the secondary,
`=I_(2)^(2)R_(2) = (11)^(2) xx 20 = 242W`