1MW power is to be delivered from a power station

Question:

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 the voltage to 220 V.

Solution:

(i) The power station is 10 km away from the town

Length of the Cu wire = L = 20 km = 20000 m

Resistance of Cu wire = R = 4 ohms

Current at 220 V = 0.45 × 104A

RI2 = Power loss = 4 × (0.45)2 × 108 W > 10W

The above method cannot be used as the power loss is much large.

(ii) When power P = 10W is transmitted at 11000 V

V’I’ = 106 W = 11000 I’

Current drawn = I’ = 1/1.1 × 102

Power loss = I’2R = 1/1.21 × 4 × 104 = 3.3 × 104 W

Fraction of power loss = 3.3 %

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