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

(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 11000 V, power transmitted, then a step-down transformer is used to bring voltage to 220 V.


(ρcu = 1.7 × 10-8 SI unit)



Given:
Power: P = 1 MW = 106 W
Radius of the Cu wires: r = 0.5 cm = 0.005 m
Voltage :V = 220V
Voltage boosted by step up transformer: V1 = 11000 V
Resistivity of Cu wire: ρcu = 1.7 × 10-8 SI unit
Formula used:
(i)
Power is given as
P = VI
Here, V is the voltage and I is the current.
At V= 220 V


Also,

Here, R is the resistance of the wire, ρ is the resistivity of the wire, A is the area of cross section and l is the length of the wire.
Here, l= 10km× 2 = 20000 m


Now, Power loss = I2R
We see that Power loss is way more than power delivered to the town, which is not feasible.
(ii)
Voltage boosted to 11000 V
Current becomes


Resistance would remain the same,
Thus power loss would be




Fraction of power loss would be in %


Here, Power loss is minimal.
Hence it is feasible.

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