I was told that, in an simple electronic circuit (consist of resistor and battery), the power supplied by the battery must be equal to the power (heat) dissipated by the resistor. In form of equation: VI = RI^2 ,where V=voltage supplied by the battery, I=current, R=resistence. I find that, this equation is based on 1 assumption: on average, the electron will end up with ZERO kinetic energy when it reach the terminal of positive. In other words, all the energy it gains from the battery will be used up competely to overcome the collision and other resistence along the circuit. My qeustion is, has the assumption I mention here been made? If yes, what GUARANTEE that on average all the kinetic energy must be used up after completing a circuit? I think, there is a possibility for the elctrons that, after several collisoon, they may have some "residual" kinetic energy and they continue to reach the positive terminal.The consequesce is, these powerful electron will collide with the positive terminal of battery and hence stop there by losing their kinetic energy in form of heat. This is supported by the fact that, after some time, the battery will be heated up.