1MW 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 power transmitted if
(a) power is transmitted at 220V. Comment on the feasibility of doing this.
(b) a step-up transformer is used to boost the voltage to 11000 V, power transmitted, then a step-down transformer is used to bring voltage to 220 V.
`(rho_(cu)=1.7xx10^(-8)` SI unit )

Explanation

(a) Length of copper wire = 2 x 10 km =20 km
`therefore` L=20000 m
Resistance of copper wire,
`R=rho l/A=rho l/(pir^2)`
`=(1.7xx10^(-8)xx20000)/(3.14xx(0.5xx10^(-2))^2)`
`=(3.4xx10^(-4))/(3.14xx0.25xx10^(-4))`
`=4.3312 Omega approx 4 Omega`
P=VI `rArr I= P/V=10^6/220 = 0.45 xx 10^4` A
Power loss = `I^2R=(0.45xx10^4)^2xx4`
`=0.8263xx10^8`
`approx 82.63xx10^8` W
Power loss is greater than 1 MW, so this method cannot be used for transmission.
(b) When power 1 MW is transmitted at 11000 V, V.I.=`10^6` W =11000 I.
but current,
`I.=P/(V.)=10^6/11000=1000000/11000=1/11xx10^3` A
power loss `=(I.)^2R = 1/121 xx 10^6 xx 4`
`=0.03305xx10^6`
`approx` 33050 W
Fraction of power loss = `33050/10^6xx100%`
=3.3 %