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.

Kirchhoff’s voltage law example

In this example, we have two closed loop that are 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 two formulas with Kirchhoff’s voltage law :

The formula for the left loop is :

V_{1} + V_{2} + V_{3} + V_{5} = 0

The formula for the right loop is :

V_{3} + V_{4} = 0

The results are based on the orientation of the arrow on the picture. Having the arrow in the incorrect direction is not an issue when you are solving problems using Kirchhoff’s voltage law. Instead of having a positive value for the voltage, you will get a negative value for the voltage which means the current direction is in the opposite direction of the arrow. The best example is the right loop. If you solve this loop, you get V_{3} + V_{4} = 0. But we know that the current flowing into the resistor of V_{3} is in the opposite direction of this arrow because of the position of the voltage source and this is why you will get a negative value for V_{3}.