5A high-voltage transmission line carries 500,000 volts and delivers a current of 200 amperes. If the resistance of the line is 0.02 ohms per kilometer, and the total length is 150 kilometers, calculate the total power loss in the line due to Joule heating.

Sun, 03 May 2026 03:29:49 +0000

**Understanding the Hidden Energy Losses in America’s Transmission Backbone**
As energy demand rises and discussions shift toward modernizing the U.S. power grid, more people are tuning in to how electricity flows across vast networks. The quiet transfer of high-voltage electricity over thousands of miles underpins everyday life—from powering homes in sunny California to supporting industrial hubs in the Midwest. Yet behind the smooth delivery of electricity at 500,000 volts lies a subtle but significant challenge: energy loss through resistance in transmission lines. When current travels through conductive materials like copper or aluminum, even at high voltages, a small amount of energy is lost as heat. This Joule heating, governed by Ohm’s Law, depends on the resistance of the conductor, the current, and the distance traveled. For a major 5A transmission line spanning 150 kilometers with 0.02 ohms per kilometer resistance, the cumulative effect reveals where grid efficiency truly begins. **Why This Matters Now in the U.S. Energy Landscape**
Recent trends in grid modernization and renewable integration spotlight this challenge. As the nation pivots toward wind and solar farms often located far from population centers, longer transmission distances compound energy losses. Public interest grows as discussions around reliability, sustainability, and infrastructure investment center on minimizing waste—not just reducing carbon, but improving every mile of power flow. **How Joule Heating Transforms Power Delivery**
Power loss in transmission lines is calculated using a simple formula: *P_loss = I² × R_total*. With an iron CL overflowing at 200 amperes, and a total resistance emerging from resistivity per kilometer multiplied by 150 kilometers, the calculation becomes striking. That 0.02 ohm resistance per kilometer multiplies neatly to 3 ohms total—solid for 150 km. At 200 amperes, this resistance triggers measurable energy dissipation.