Kirchhoff's loop rule review

Kirchhoff’s loop rule states that the sum of all the electric potential differences around a loop is zero. It is also sometimes called Kirchhoff’s voltage law or Kirchhoff’s second law. This means that the energy supplied by the battery is used up by all the other components in a loop, since energy can’t enter or leave a closed circuit. The rule is an application of the conservation of energy in terms of electric potential difference, $\Delta V$delta, V.

Mathematically, this can be written as:

For example, we can use Kirchhoff’s loop rule to find the unknown electric potential difference across a resistor (Figure 1).

Let’s pick our starting point at the battery and go around the loop until we are back to the same point.

The electric potential increase over the battery is $\epsilon$\epsilon. Over $R_1$R, start subscript, 1, end subscript there is an electric potential decrease of $V_1$V, start subscript, 1, end subscript. We do not know the electric potential decrease $V_2$V, start subscript, 2, end subscript over $R_2$R, start subscript, 2, end subscript.

Now we can use the loop rule to solve for $V_2$V, start subscript, 2, end subscript in terms of $V_1$V, start subscript, 1, end subscript and $\epsilon$\epsilon:

For deeper explanations, see our video on Kirchhoff's loop rule (or voltage law).

To check your understanding and work toward mastering these concepts, check out our exercises: