Content Correction: Between 06:35 and 06:46 the signs of the slope on the slide are wrong. The partial derivative of V'_H with respect to P should be smaller than 0 and that of V'_L should be greater than 0.
Some remarks: 1. The Kirchhoff's current law in 08:45 can be derived from conservation of electric charge ( en.wikipedia.org/wiki/Charge_conservation ) at an infinitesimally small control volume surrounding the node considered. Since inside a conductor electric charges can move freely, the net charge must be 0 everywhere in the power line, so we can drop the time derivative term in the charge density continuity equation. Kirchhoff's current law can then be deduced by applying divergence theorem to the divergence term of the charge density continuity equation. 2. Y_eq in 10:58 is a Laplacian matrix ( de.wikipedia.org/wiki/Laplace-Matrix ) in graph theory. In a well-connected grid where all n nodes are connected to each other by at least 1 path, the rank of the corresponding Laplacian matrix will always be n-1. We will discuss more on this in the part 3 and part 3.5 of this series: th-cam.com/video/jn4dKlzjHAQ/w-d-xo.html th-cam.com/video/DrsbsygaCAE/w-d-xo.html
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Content Correction:
Between 06:35 and 06:46 the signs of the slope on the slide are wrong. The partial derivative of V'_H with respect to P should be smaller than 0 and that of V'_L should be greater than 0.
Great summary, thank you for making this video!
Some remarks:
1. The Kirchhoff's current law in 08:45 can be derived from conservation of electric charge ( en.wikipedia.org/wiki/Charge_conservation ) at an infinitesimally small control volume surrounding the node considered. Since inside a conductor electric charges can move freely, the net charge must be 0 everywhere in the power line, so we can drop the time derivative term in the charge density continuity equation. Kirchhoff's current law can then be deduced by applying divergence theorem to the divergence term of the charge density continuity equation.
2. Y_eq in 10:58 is a Laplacian matrix ( de.wikipedia.org/wiki/Laplace-Matrix ) in graph theory. In a well-connected grid where all n nodes are connected to each other by at least 1 path, the rank of the corresponding Laplacian matrix will always be n-1. We will discuss more on this in the part 3 and part 3.5 of this series:
th-cam.com/video/jn4dKlzjHAQ/w-d-xo.html
th-cam.com/video/DrsbsygaCAE/w-d-xo.html
You're so slow man, nobody is gonna listen this an leave the video without watching. Make it better.