# Joule heating due to the (slow) electron drift velocity?

I understand the concept of why the signal speed is higher than the electron drift velocity, but I can't understand the concept of joule heating. If electrons move slow then how do they produce a lot of heat when they hit the nucleus. Besides my friend once told me that the drift velocity is the net movement and electrons move fast in all directions, if that is the case why do they move like that?

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The absolute velocity of the electrons actually doesn't matter for joule heating. Think about it this way, if there is no current flowing there wouldn't be any joule heating. So, even if electrons are moving quickly and randomly when no current is flowing, we know no joule heating would occur and that joule heating is really about the net change in effect caused by the current. That is, the base electron velocity doesn't have an effect. All that matters is the $\Delta V$ over the base electron velocity which is given by the drift velocity.
Via Ohm's Law you can see that $P_{ower} = I^2 R$ so it's no wonder that heat generation is proportional to $I^2 R$.