Kirchhoff's voltage law (KVL) [Derivation from Maxwell's Equations]

Topic: In this video we will derive Kirchhoff's voltage law (KVL) for direct current (DC) by using one of the four Maxwell's Equation (Faraday's Law of Induction with constant magnetic field).
We will also need the Stokes' theorem to turn a surface integral into a path integral.

[@jorgearturomartinezsanchez4882]

Amazing! You could also use that E comes from a scalar potential and skip all the part where you make it constant by using the fundamental theorem of line integrals.

[@valmormn]

This is gold!

[@anshsrivastava61]

Your voice is like Mike from breaking bad

[@vaishnavivishnubhotla7748]

Thank you. It is of great help.

[@user-ub1qi3ye5k]

Incredible

[@GnomeInvasion]

Great video. I understood the mathematics just fine, but I didn't quite understand the constant electric field part, it'd be great if someone could explain. P.S: I'm a math major who hasn't bothered with physics for a while, oh category theory... how you've ruined my intuition x)

[@MrYouMath]

GnomeInvasion We assume that the magnetic field is constant/stationary hence it doesn't change with time. That is the reason why the left hand side is equal to zero. The next assumption was that i assumed that in the resistors the electric field is parallel to the boundary of the surface. Assuming the electric field to be constant, hence the voltage drop per length is constant.

[@GnomeInvasion]

MrYouMath Thank you.

[@yosefpatinio3669]

In the case of AC circuit , how KVL still works? if there is a changing magnetic field inside the loop?

[@ApertureScience_Opt]

Strictly speaking, KVL does not work. However, it can be expressed through an equivalent voltage source or current source. Otherwise you have to solve Maxwell's equations. This is because Kirchhoff's law is a special situation of Maxwell's equations.

[@ApertureScience_Opt]

Circuit theorems are basically intended to avoid directly solving Maxwell's equations and to represent them as nodes and branches by applying graph theory.