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 power transimitted if (i) power is transformer is used to boost the voltage to 11000 V, power transmitted, then a step down transformer is used to bring voltages to 220 V. `(rho_(Cu) = 1.7 xx 10^(-8) SI`unit)

Options

A. `1.8%`
B. `1.5%`
C. `3.6%`
D. `7.2%`

Answer

C

Explanation

Given, `l=20 km = 20xx10^(3)m`
`r=0.5 cm =0.5xx10^(-2)m, rho = 1.7xx10^(-8)Omega m`
`R=(rho l)/(A)=(1.7xx10^(-8)xx20xx10^(3))/(3.14xx(0.5xx10^(-2))^(2))=4.3 Omega`
`P=10^(6)W, V=11000 V`
`I=(P)/(V)=(10^(6))/(11000)=(10^(3))/(11)A`
Power loss, `I^(2)R=((10^(3))/(11))^(2)xx4.3=3.6xx10^(4)W`
`(P_("LOST"))/(P_("TRANSMITTED"))xx100%=(3.6xx10^(4))/(10^(6))xx100=3.6%`