1 MW power is to be delivered from a power station to a town 10 Km away. One uses a pair of Cu wires of radius 0.5 cm for this purpose.
Calculate the fraction of ohmic losses to the power transmitted if;

(i) power is transmitted at 220V. Comment on the feasibility of doing this.

(ii) a step-up transformer is used to boost the voltage to 11000V, power transmitted, then a step-down transformer is used to bring a voltage to 220 V.                                       ρcu=1.7×10-8SIunit

Hint: The power losses depend on the current flowing in the wires.
(i) Step 1: The town is 10 km away, length of pair of Cu wires used, L=20 km=20000 m.
ResistaneofCuwires,R=ρlA=ρlπ(r)2
=1.7×10-8×200003.14×0.5×10-22=4Ω
At220V,VI=106W;I=106220=0.45×104A
Powerloss=RI2
=4×0.452×108W
>106W
Therefore, this method cannot be used for transmission.
Step 2:
(ii)WhenpowerP=106Wistransmittedat11000V,
V'I'=106W=11000I'
Currentdrawn,I'=11.1×102
Powerloss=RI2=11.21×4×104
=3.3×104W
Fractionofpowerloss=3.3×104106=3.3%