Problem 2 A small town requires 5 MW of power, that must be delivered from 50km

Question

Problem 2 A small town requires 5 MW of power, that must be delivered from 50km away over power lines with a resistance per unit length of 30 /in (a) Assume the power is transmitted to the town at 10kV i. How much current does this correspond to at this voltage? ii. This amount of current must pass through the transmission nes. How much power will be dissipated in the transmission process due to the resistance of the wire (b) Now assume the power is transmitted to the town at 500 kV. i. How much current does this correspond to at this voltage? ii. How much power will be dissipated in the transmission process due to the resistance of the wire? (c) Which option is more efficient for delivering power? Explain your answer using the relations between current, power, and voltage that you used to find your results from above

Explanation / Answer

a)

i) we know, P = V*I

I = P/V

= 5*10^6/(10*10^3)

= 500 A

ii)
Total resistance of the wires, R = 2*30*10^-6*50*10^3

= 3 ohms

Power dissipated = I^2*R

= 500^2*3

= 7.5*10^5 W or 0.75 MW

b)

i) I = P/V

= 5*10^6/(500*10^3)

= 10 A

ii)

Power dissipated = I^2*R

= 10^2*3

= 300 W

c) The seond option is efficient as there is less power dissipation through transmision lines.

I = P/V

and power dissipated = I^2*R

= (P/V)^2*R

so power dissipation is inverly proportional to V^2

if V is increasesd to 10 times power dissipation becomes 1/100 times.

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