A high-voltage transmission line carries 1000 A starting at 700 kV for a distance of 100 mi. If

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A high-voltage transmission line carries 1000 A starting at...

A high-voltage transmission line carries $1000 \mathrm{A}$ starting at $700 \mathrm{kV}$ for a distance of $100 \mathrm{mi}$. If the resistance in the wire is $0.500 \Omega / \mathrm{mi},$ what is the power loss due to resistive losses?

Key Concepts

Joule Heating

Joule heating is the process by which electrical energy is converted into thermal energy (heat) in a conductor due to its resistance. The power loss associated with this heating is determined by the formula P = I²R, where I is the current through the conductor and R is its resistance. This concept is fundamental in evaluating energy losses in electrical circuits and systems.

Resistance Calculation

In many electrical applications, especially with extended conductors like transmission lines, the total resistance is calculated by multiplying the resistance per unit length by the length of the conductor. This simple but crucial concept allows engineers to determine how much resistive loss to expect over a given distance.

High Voltage Transmission

High voltage transmission is used in power distribution systems to minimize energy losses. By transmitting power at a high voltage, the current required for a given power level is reduced, which in turn reduces resistive losses since these losses are proportional to the square of the current. This approach is essential for maintaining efficiency in long-distance power delivery.

Power Loss in Transmission Lines

Understanding power loss in transmission lines involves calculating the energy lost due to the resistance of the lines. It combines the concepts of Joule heating and the total resistance of the line, emphasizing the importance of both current management and material properties in reducing unwanted energy dissipation along the transmission route.

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