# Kirchoff's Loop Rule

Kirchoff's Loop Rule:

Around any circuit loop, apply energy conservation in the form of

What in the world does that mean? And how does that tie in with energy conservation?

Remember that voltage -- or electric potential difference -- is the potential energy per unit charge. So any description of electric potential -- or voltage -- is very closely connected with energy.

Consider a very simple circuit like this:

Think of walking around this circuit while carring a charge q. Start at a and "walk" through the battery to b. The potential energy of the charge has increased by an amountqV. As you walk on to c nothing happens. As you walk through the resistor -- from c to d -- the resistor heats up. You give up the potential energy of the charge to the resistor. As you walk back from d to a, nothing happens.

The electric potential V that is "gained" in going through the battery is "lost" in the potential difference across the resistor IR.

That is all that Kirchoff's Loop Rule says. As you "walk" around any complete loop in the circuit -- coming back to where you started -- the potential energy you gain must equal the potential energy you loose. Or the sum of the electric potential differences must be zero. Or the sum of the positive electric potential differences must equal the sum of the negative electric potential differences.

Or -- the sum of all the potential differences due to the batteries must equal the sum of all the potential differences across the resistors. That is,

Actually, in a more complicated circuit, that V should really be the sum of the V's or