Hi, I have just started studying EM induction and I got stuck with the derivation of potential difference across a solenoid when the current in it is changing. My textbook (Physics for Scientists and Engineers by Tipler) derives it in very mathematical way just by saying that because the induced EMF in solenoid is equall to -L*dI/dt and the decrease in potential due to the resistance of the solenoid is -Ir the totel potential difference is -L*dI/dt - Ir. However I would prefere using the Lenz's Law for deriving the direction of induced EMF. So I say that because the current is in some direction it causes a decrease in potential in that direction due to the resistance. That is -Ir. But because the induced current wants to oppose the original current, the induced EMF and the potential difference due to resistance would have opposite signs. That means that the total potential difference across a solenoid would be abs(LdI/dt - Ir). Where have I made a mistake? Thanks for your help.