Question

PG&E needs to send 100MW to Davis over transmission lines that are many miles long--so long that the resistance is not completely negligible (let's say 0.001?). Given that the product VI needs to be 100MW, PG&E could send this power at low voltage and high current, or at high voltage and low current. If you use as the power dissipated in the lines, it seems like high voltage is bad--it leads to a lot of power wasted in the transmission lines--yet you probably know that the transmission lines are indeed high-voltage. Explain how high-voltage lines actually lead to smaller losses in the lines.

R

Answer 1

Transmission losses = I²R,

where,

R is the resistance of the transmission cables

I is the current in the transmission cable

P = I V

where,

V is the voltage

Therefore, high voltage means low current for the same power transmission.

For example, increasing the voltage by a factor of ten, while holding power constant, decreases your resistive losses by a factor of a hundred. This is how high-voltage lines actually lead to smaller losses in the lines.