Resistance Basics

A copper transmission line carrying 1,000 amps gets warm. That heat is wasted energy, lost on the way from the power plant to your house. In recent years, U.S. transmission and distribution losses have totaled about 5% of all electricity generated, roughly 200 TWh, enough to power about 18 million homes. Resistance is the cause.

Resistance is a material's opposition to current flow, measured in ohms (Ω). It arises because electrons collide with atoms as they move through a conductor, losing energy as heat. Ohm's Law (V = IR) connects the three fundamental electrical quantities: voltage drives current through resistance. Higher resistance means less current for the same voltage.

Resistance depends on four factors: the material (copper resists less than aluminum), the length (longer wires have more resistance), the cross-sectional area (thicker wires have less resistance), and temperature (hotter wires resist more). Power lost to resistance equals P = I²R: it scales with the square of current. This is why high-voltage transmission works: doubling voltage halves the current for the same power, reducing resistive losses by a factor of four.

Worked Example

A 100-km transmission line has total resistance of 5 ohms and carries 500 amps.

• Calculate power loss. P = I²R = 500² x 5 = 1,250,000 W = 1.25 MW.
• If voltage is doubled (halving current to 250 A for the same power), recalculate loss. P = 250² x 5 = 312,500 W = 0.3125 MW.

Doubling voltage reduced losses from 1.25 MW to 0.31 MW, a factor of what?

Four (1.25/0.3125 = 4). Losses scale with I². Halving current cuts losses to one-quarter. This is why transmission lines operate at the highest practical voltage.

Resistance and I²R losses are the physical constraints that shaped the entire design of the modern power grid.

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