# Lesson : Kirchhoff’s voltage law

Kirchhoff’s voltage law or loop (mesh) rule states that the sum of voltages in a closed loop will be equal to 0.

$\sum\limits_{i=1}^n V_{i}=0$

where n is the total numbers of voltage in the loop. Voltage gain in a loop (voltage source are an example) will have a positive value and voltage drop will have a negative value.

In this example, we have one closed loop that is going to be analyse. Kirchhoff’s voltage law speculates that the sums of voltages in a closed loop will be equal to 0. In this specific example, we can find one formulas with Kirchhoff’s voltage law.

$\sum\limits_{i=1}^n V_{i}=0$

Voltage gain will have a positive value and voltage drop will be negative. $V_{1}$ is a voltage source and therefore will be positive since we gain voltage. $V_{2}, V_{3} \ and \ V_{4}$ are voltage drop. With this information and Kirchhoff’s voltage law we can find the formula below:

$V_{1} - V_{2} - V_{3} - V_{4} = 0$

We can rearrange this formula to isolate $V_{1}$:

$V_{1} = V_{2} + V_{3} + V_{4}$

The example above is very simple. In the next lessons, we will see another law of Kirchhoff’s which is the current law. After that lessons, we will see that Kirchhoff’s voltage law and current law are very useful to solve circuits that contains series and parallel circuits mixed together.