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)

Answer

A

Explanation

i) The town is 10 km away, length of pair of Cu wires used, L=20km = 200000m.
Resistance of Cu wires, `R=l/A = l/(pi(r )^(2))`
`=(1.7 xx 10^(-8) xx 20000)/(3.14(0.5 xx 10^(-2))^(2))=4 Omega`
I at 220 V `VI = 10^(6)W, I=(10^(6))/(220)=0.45 xx 10^(4)`A
`RI^(2)`=Power loss
`=4 xx (0.45)^(2) xx 10^(8)`W
`gt10^(6)W`
Therefore, this method cannot be used for transmission.
ii) When power `P=10^(6)` W is transmitted at 11000 V.
`V^(')I^(')=10^(6)W = 11000I^(')`
Current drawn, `I^(') = 1/(1.1) xx 10^(2)`
Power loss = `RI^(2)=1/(1.21) xx 4 xx 10^(4)`
`=3.3 xx 10^(4)W`
Fraction of power loss =`(3.3 xx 10^(4))/(10^(6))=3.3%`