When electricity is transported from a power station to a city, the line voltage (relative to ground) is usually on the order of several hundred thousand volts. A power line cable has a radius of a = 2.0 cm, is made of aluminum with a resistivity of ρ = 2.7×10−8 Ω ⋅ m, and spans a distance of l = 100 km from a power station to a city. The city consumes 100 MW of power (so I2RL =100MW). (a) Find the resistance of the power cable between the station and the city(i.e.,between points A and B). (b) Suppose that the line voltage ∆VBC = 120 V. i. How much current is required to flow through the power line to deliver 100MW of power to the city? ii. How much energy is lost as heat between points A and B? (c) Suppose that the line voltage ∆VBC = 300 kV. i. How much current is required to flow through the power line to deliver 100MW of power to the city? ii. How much energy is lost as heat between points A and B?
When electricity is transported from a power station to a city, the line voltage (relative to ground) is usually on the order of several hundred thousand volts. A power line cable has a radius of a = 2.0 cm, is made of aluminum with a resistivity of ρ = 2.7×10−8 Ω ⋅ m, and spans a distance of l = 100 km from a power station to a city. The city consumes 100 MW of power (so I2RL =100MW). (a) Find the resistance of the power cable between the station and the city(i.e.,between points A and B). (b) Suppose that the line voltage ∆VBC = 120 V. i. How much current is required to flow through the power line to deliver 100MW of power to the city? ii. How much energy is lost as heat between points A and B? (c) Suppose that the line voltage ∆VBC = 300 kV. i. How much current is required to flow through the power line to deliver 100MW of power to the city? ii. How much energy is lost as heat between points A and B?
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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When electricity is transported from a power station to a city, the line voltage (relative to ground) is usually on the order of several hundred thousand volts.
A power line cable has a radius of a = 2.0 cm, is made of aluminum with a resistivity of ρ = 2.7×10−8 Ω ⋅ m, and spans a distance of l = 100 km from a power station to a city. The city consumes 100 MW of power (so I2RL =100MW).
(a) Find the resistance of the power cable between the station and the city(i.e.,between points A and B).
(b) Suppose that the line voltage ∆VBC = 120 V.
i. How much current is required to flow through the power line to deliver 100MW of power to the city?
ii. How much energy is lost as heat between points A and B?
(c) Suppose that the line voltage ∆VBC = 300 kV.
i. How much current is required to flow through the power line to deliver 100MW of power to the city?
ii. How much energy is lost as heat between points A and B?
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