Direction of current in a LR circuit
It seems that when I do tasks I always just assume I' has the same sign as I. But actually this is not true?


If you consider a sinusoidal stimulus, it will only be true for half the cycle.

But you should still use

$$ U = I'L + IR $$

because when the signs of \$I'\$ and \$I\$ are opposite, they will have opposite effect on the potential difference across the part, just as the equation says.