Kirchhoff's Laws:

Within all of the circuits examined so far, Ohm's Law declares the relationship among voltage, current, and resistance. These circuits have been relatively simple in nature.  Several circuits are extremely complex and cannot be solved along with Ohm's Law. These circuits have various power sources and branches that would make the use of Ohm's Law impossible or impractical.

By experimentation in the year of 1857 the German physicist Gustav Kirchhoff developed methods to solve complex circuits. He developed two results, known today as Kirchhoff's Laws.

Law 1: A sum of the voltage drops around a closed loop is equal to the sum of the voltage sources of that loop (Kirchhoff's Voltage Law).

Law 2: A current arriving at any junction point in a circuit is equal to the current leaving which junction (Kirchhoff's Current Law).

Kirchhoff's two laws might seem obvious based on what we already know about circuit theory. Even by they might seem extremely easy, they are powerful tools in solving complex and hard circuits.

Kirchhoff's laws could be associated to conservation of energy and charge if we look at a circuit along with one load and source.  Because all of the power gives from the source is consumed through the load, charge and energy are conserved.  Because voltage and current could be associated to charge and energy, after that Kirchhoff's laws are only restating the laws governing energy and charge conservation.

The mathematics included becomes more hard as the circuits become more complex. Thus, the discussion here will be limited to solving only associatively simple circuits.