system
Given the following post, respond as if you're commenting on Reddit:
human
In alternating current, how is electricity carried in one direction (from the power source to the electrical device) if the current is constantly changing direction?
gpt
Take a circuit that's just an AC power source connected to a resistive load.

The power source provides a voltage V(t) = V*_0_*cos(ωt), which is entirely dropped across an equivalent resistor of resistance R.

The current through the resistor is then I(t) = V(t)/R = V*_0_*cos(ωt)/R.

The instantaneous power dissipated in the resistor is P(t) = V(t)I(t) = V*_0_*^(2)cos^(2)(ωt)/R.

So the current is a cosine function, which has both positive and negative swings as a function of time. But the power is a cosine-**squared** function, which is never negative.

And while the current through the resistor switches direction, the power dissipation doesn't care whether the current is moving "forward" or "backward". When there is current flowing through the resistor in either direction, there is a positive power dissipated.

And if you average the current over an integer number of periods, you get zero, but if you average the power over an integer number of periods, you get something positive.