My question refers to the image below:
From what I have previously thought, in order to calculate current through a resistor you would use Ohm's Law, meaning you get the voltage across the resistor divided by the resistance of the resistor.
Usually, you can work out the voltage across a resistor using the potential divider rule, but in the cases presented in the images, you are given voltages on either side of the resistor.
So my question is, why is the lower voltage subtracted from the higher voltage? I understand that adding the two voltages would go against the conservation of energy, but I can't think of a logical or a mathematical reason for the subtraction.