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KVL and KCL (Part 2 of shamelessly stealing of Wikipedia)
What are KVL and KCL? To begin with, KVL stands for "Kirchoff's Voltage Law", and KCL stands for "Kirchoff's Current Law". These are two very fundamental yet powerful laws help analyze all the circuits that currently interest me (and quite a bit more that don't). Kirchoff's Voltage law states that the sum of any potential differences around any closed loop is zero.
Example of KVL: In this circuit, the resistors are connected in series. The voltage sum across the loop is zero; -B1_v+R1_v+R2_v=0
Kirchoff's Current law states that the sum of all currents within a junction (a point) are equal to zero. Example of KCL: In this circuit, the resistors are connected in parallel. The sum of currents for NODE1 equals zero. -B1_I+R1_I+R2_I=0
While these two laws do not appear useful, we shall soon encounter a problem in which parallel-series analysis will not be applicable - but we shall see how KVL and KCL apply.
A final note; these laws are an extension of Ohm's law - and analgous to the first theorem of thermodynamics - energy is always conserved.