Question

An AC power generator produces 51 A (rms) at 3,600 V. The voltage is stepped up to 100,000 V by an ideal transformer, and the energy is transmitted through a long-distance power line that has a resistance of 114 Ω. What percentage of the power delivered by the generator is dissipated as heat in the power line?

%

Answer 1

here,

the voltage of primary , Vp = 3600 V

the current in primary , Ip = 51 A

the voltage in seccondary , Vs = 100 000 V

let the current in the seccondary be Is

power = Vp * Ip = Vs * Is

3600 * 51 = 100 000 * Is

Is = 1.84 A

the power of primary , Pp = Vp * Ip

Pp = 3600 * 51 = 1.84 * 10^5 W

the power dissapated in resistance , Po = Is^2 * R

Po = 385.9 W

the power delivered by the generator is dissipated as heat in the power line , % = (Pp - Po)/Pp * 100

% = ( 184000 - 385.9)/184000 * 100

% = 99.8 %