Question

A power plant produces an rms voltage of Vp = 12.0 x 10^3 V and an rms current of Ip = 180 A. The rms voltage is stepped up to 300 x 10^3 V by a transformer before it is transmitted to a substation. The resistance of the transmission line is between the power plant and the substation is R = 1000Ω.

a) What is the turns ration Ns/Np for this transformer?

b )What is the rms current in the transmission line (secondary) from the plant to the substation?

c) What percentage of the power produced at the power plant is lost during the transmission? {Hint: calculate the power generated and the power lost (from the rms values either given or obtained above), then take the ratio of Plost/Pgen and multiply by 100%}

% loss =

Answer 1

a) Ns/Np = Vs/Vp

= 300*10^3/(12*10^3)

= 25 <<<<<<<<<<<----------------Answer

b) use, Vp*Ip = Vs*Is

==> Is = Vp*Ip/Vs

= 12*10^3*180/(300*10^3)

= 7.2 A <<<<<<<<<<<----------------Answer

c) P_gen = Vp*Ip

= 12*10^3*180

= 2.16*10^6 W

P_lost = Is^2*R

= 7.2^2*1000

= 51840 W

percentage of power lost = (P_lost/P_gen)*100

= (51840/(2.16*10^6))*100

= 2.4 % <<<<<<<<<<<----------------Answer