An electricity-generating station needs to deliver 20 MW of power to a city 1.0 km away. A common voltage for commercial power generators is 22 kV, but a step-up transformer is used to boost the voltage to 230 kV before transmission.

(a) If the resistance of the wires is 2.0 ohms and the electricity costs about 10 cents/kWh, estimate what it costs the utility company to send the power to the city for one day?

Question

Lily Hess

Physics

29 October, 17:14

An electricity-generating station needs to deliver 20 MW of power to a city 1.0 km away. A common voltage for commercial power generators is 22 kV, but a step-up transformer is used to boost the voltage to 230 kV before transmission.

(a) If the resistance of the wires is 2.0 ohms and the electricity costs about 10 cents/kWh, estimate what it costs the utility company to send the power to the city for one day?

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Answers (1)

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Christopher Velazquez · Answer 1

Power to be transferred = 20 x 10⁶ W.

Voltage at which power is transferred V = 230 x 10³ V.

If current in the carrying wire is I

V x I = Power

230 x 10³ x I = 20 x 10⁶

I = 86.9565 A

Power loss in the transmission line

I² R, I is current and R is resistance

= 86.9565² x 2

= 15122.86 W

= 15.123 KW

In one day power loss

= 15.123 x 24 kWH.

= 363 kWH.

Cost = 363 x 10

= 3630 cent

= 36.30 dollar.