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Gustav Kirchhoff (1824-1887) was an accomplished Prussian physicist and instrument maker, and best known for his current and voltage circuit laws. Kirchhoff’s first circuit law, known as his current law, states that the algebraic sum of currents in a network of conductors meeting at a point is zero. Kirchhoff’s second circuit law, known as his voltage law, states that the sum of the voltages, taking into account their polarities, in a closed circuit is zero.

Kirchhoff’s current law is based on conservation of charge, measured in coulombs, which is current integrated over (multiplied by) time. SPICE and similar circuit simulation software make use of a matrix version of Kirchhoff’s current law along with Ohm’s law to perform nodal analysis of more complex circuits. So you would think that at this point, there is little that is controversial about Kirchhoff’s laws. That brings us to a series of YouTube videos that, surprisingly, explore the idea that Kirchhoff’s laws might not hold under certain circumstances.

>Gustav Kirchhoff (1824-1887) was an accomplished Prussian physicist and instrument maker, and best known for his current and voltage circuit laws. Kirchhoff’s first circuit law, known as his current law, states that the algebraic sum of currents in a network of conductors meeting at a point is zero. Kirchhoff’s second circuit law, known as his voltage law, states that the sum of the voltages, taking into account their polarities, in a closed circuit is zero. >Kirchhoff’s current law is based on conservation of charge, measured in coulombs, which is current integrated over (multiplied by) time. SPICE and similar circuit simulation software make use of a matrix version of Kirchhoff’s current law along with Ohm’s law to perform nodal analysis of more complex circuits. So you would think that at this point, there is little that is controversial about Kirchhoff’s laws. That brings us to a series of YouTube videos that, surprisingly, explore the idea that Kirchhoff’s laws might not hold under certain circumstances.

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The section of wire where the current is being induced is essentially turned into an active component, like that battery. Its being drawn as a stright line is a distraction to keep you from thinking it's an active component.

Agreed.