When a current flows through a resistor, taken as a system, there is a work transfer into the system. This is because the current can drive a motor, the motor can drive a pulley and the pulley can raise a weight.
The current flow, I, in amperes, is given by
I= dC / dt
Where C is the charge in the coulombs and t is time in seconds. Thus the dC is the charge crossing a boundary during time dt. If E is the voltage potential, the work is
dW = E.dC = EI dt
W = lim dt --->0 ( dW / dt ) = EI
This is the rate at which work is transferred.
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