Question

Fifteen megawatts of electricity is to be transmitted over a power line of resistance 3 ohms.

a) If the electricity is generated at 10,000 V and is to be transmitted at 200,000 V, what should be the ratio of turns of the transformer?

b) At what current will the power be transmitted?

c)What percentage of the original power will be lost in the line because of resistive heating?

Answer 1

Given:

Power to be transmitted, P = 15 MW = 15 x 106 W

Resistance of power line, r = 3Ω

Primary voltage, Vp = 10000 V

Secondary voltage, Vs = 200000 V

a) For a transformer, Np/Ns = Vp/Vs

Where, Np-number of turns in primary coil of transformer

                Ns- number of turns in secondary coil of transformer

Vp/Vs = 10000/200000 = 0.05

Answer; ratio of turns of transformer, Vp/Vs = 0.05

b) Power, P = Vs Is

Current, Is = P/Vs= 15 x 106 /200000 = 75 A

Answer: current with which power transmitted, Is = 75A

c) Power lost due to resistive heating, Ps = Is2 r= 75x75x3=16875W

Percentage of initial power lost due to heating, dP = ( Ps)/P x 100%

dP =( 16875) x 100/15 x 106 = 0.112 %

Answer : Percentage of initial power lost due to heating = 0.112 %