Kirchhoff's voltage law (KVL)
The sum of all the voltages around the loop is equal to zero. v1 + v2 + v3 - v4 = 0
This law is also called Kirchhoff's second law, Kirchhoff's loop (or mesh) rule, and Kirchhoff's second rule.
Similarly to KCL, it can be stated as:
sum_{k=1}^n V_k = 0
Here, n is the total number of voltages measured. The voltages may also be complex:
sum_{k=1}^n tilde{V}_k = 0
This law is based on one of the Maxwell equations, namely the Maxwell-Faraday law of induction, which tells us that the voltage drop around any closed loop is equal to the rate-of-change of the flux threading the loop. The amount of flux depends on the area of the loop and on the magnetic field strength. KVL says the loop voltage is zero. The Maxwell equations tell us that the loop voltage will be small if the area of the loop is small, the magnetic field is weak, and/or the magnetic field is slowly changing.
Routine engineering techniques -- such as the use of coaxial cable and twisted pairs -- can be used to minimize stray magnetic fields and minimize the area of vulnerable loops. In this way things can be arranged so that KVL becomes a good approximation, even in situations where it otherwise would not have been.
