Kirchhoff's Loop Rule

Think of a circuit loop like a hiking trail that loops back to camp. Potential is elevation. Batteries push you uphill, resistors let you coast downhill as current flows through them, and when you finish the loop you are back at your starting elevation no matter how many hills and valleys you crossed. That is the whole idea: pick a starting point, walk the loop in one direction, add up every rise and subtract every drop, and the total comes out to zero.

To track this with two batteries, pick a direction to walk the loop, say clockwise, and pick a starting point. At each battery, you gain voltage equal to its EMF if you cross from its minus terminal to its plus terminal, and you lose voltage if you cross from plus to minus. At each resistor, you lose voltage equal to i times R if you walk in the same direction as the current, and gain it if you walk against the current. Add everything up, set it equal to zero, and solve for whatever is unknown. The direction you chose to walk is just bookkeeping. It does not change the physics, only the signs you write down.

This rule is Kirchhoff's junction rule's partner: the junction rule conserves charge at a point, while the loop rule conserves energy around a path. Together they give enough equations to solve any circuit, no matter how tangled. The loop rule also explains why adding a second resistor in series makes a bulb dimmer: the same battery voltage now has to cover two drops instead of one, so less current flows through each.