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The number of electrons flowing through a circuit is called the current (10 ^23 electrons per second is called 1 ampere- From memory, could be wrong). The acceleration is due to the Electro Motive Force measured in Volts. So can have the same amount of energy with a large current and a small EMF or a small current and a large EMF W =A X V.
Frank
Increase in speed of electrons directly translates to increase in current. Current may be viewed as number of electrons passing a particular point in unit time. In other words, if I somehow increase the number of electrons crossing a point in a unit time, I have increased the current.
One of the ways to increase in speed of electrons is by increasing the corresponding electric field. To increase the electric field, we can either increase the voltage or reduce the length of the wire. As we understand, Electric field E = V/d, where V is applied voltage, d is the separating distance.
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