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My friend said this to me and just want to make sure this is right " when we connect the a battery to a LED and the 2 poles are connected, electrons flow from the (-) to the (+) but with very low velocity, but when you do the same with a capacitor , once the 2 plates are connected electrons flow incredibly fast that's why it's discharged fairly quickly" is that true?

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In a word, no. The drift velocity is always very small in common circuits (~$10^{-4}cm/s$). In this scenario, when the plates are connected, the electrons still travel slow but all of the electrons along the wire start moving almost at the same time, so even though they move slowly, the electric charge on the plates will vanish quickly. The electrons on the negative plate move into the wire and the positive plate is filled with electrons that were previously in the wire right next to it.

This is the difference between the speed of current and the speed of the electrons. Current travels very fast (it is like the speed of sound in the free electron sea). Electrons drift very slow.

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