The Loop Rule

The second rule we can apply to a circuit is

The Loop Rule: The sum of all the potential differences around a closed loop equals zero.

Σ ΔV = 0 for a complete loop.

In a circuit there are charges moving through these potential differences, so another way to say the rule is that when a charge goes around a complete loop, returning to its starting point, its potential energy must be the same. Positive charges gain energy when they go through batteries from the - terminal to the + terminal, and give up that energy to resistors as they pass through them.

Use the loop rule to determine the current through the battery in a circuit consisting a 16-volt battery connected to a set of three resistors, a 2 Ω resistor in series with a 2 Ω resistor and a 3 Ω resistor in parallel.

Our closed loop will consist of the battery and the two 2 Ω resistors. It doesn't matter where we start, as long as we come back to the same spot. Let's go clockwise around the loop starting at the bottom left corner.

+16 V - (2 Ω)*I - (2 Ω)*3I/5 = 0

+16 V = (10 Ω)*I/5 + (6 Ω)*I/5

+16 V = (16 Ω)*I/5

This gives I = 5 A.

The loop rule is actually a conservation law in disguise. The loop rule is equivalent to the Law of Conservation of ___________?

  1. Energy
  2. Momentum
  3. Mass
  4. Charge
  5. Current

Energy. For a charge flowing around a complete loop the gains in energy are always offset by the losses - the total change in energy is the same.