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