Kirchhoff's Current and Voltage Laws

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Kirchhoff's Current Law

Kirchhoff's Current Law says that the current going into a junction is equal to the current going out of a junction. In other words, the sum of the currents entering the node must be zero (if we consider currents leaving the node to be a negative current entering the node). Consider the following diagram:

File:Kirchhoffs current law node diagram.jpg

For the node A in the center, i1 and i2 are entering the node, and i3 and i4 are leaving the node. We would write:

i1+i2+(-i3)+(-i4)=0\, which can also be written as i1+i2=i3+i4\,

Note that i7 is equal to i2; we can prove this by analyzing node B. We can also treat everything between node C and D as one big node, and conclude that i5 is equal to i6 without having to know the value of any of the currents within.

=Kirchhoff's Voltage Law

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