Krichhoff's Laws

Gustav Krichhoff (1824 - 1887) , German Physicist developed two laws based on electric theories.

Krichhoff's First Law:

"The algebraic sum of currents flowing towards a junction in an electric circuit is zero"

An algebraic sum is one which the sign of the quantity is taken into account. For example, consider six conductors carrying currents a,b,c,d,e and f meeting at a common point as shown in the figure. If we take the signs of current flowing towards the point as positive, then the current flowing away from the point will be assigned negative sign. Thus applying Krichhoff's first law the junction in figure,

             a + b + c + d + (-e) + (-f) = 0
or                               a + b + c + d = e + f

i.e.,  Incoming currents = Outgoing currents

Hence Kirchhoff's first law can also be stated as under:

The sum of the currents flowing towards any junction in an electric circuit is equal to the sum of currents flowing away from the junction.

Krichhoff's law is true because electric current is merely the flow of electrons and they  cannot accumulate at any point in the circuit.

Krichhoff's Second Law:

"In any closed circuit or mesh, the algebraic sum of all the electromotive forces (e.m.fs) and the voltage drops is equal to zero"

ie, in any closed circuit or mesh, 

Algebraic sum of e.m.fs+Algebraic sum of voltage drops = 0

The validity of Krichhoff's second law can be readily established. If we start from any point in a closed circuit, and go back to that point after going round the circuit, there is no increase or decrease in the potential. This means that the sum of e.m.fs of all the sources met on the way plus the voltage drops in the resistances must be zero.

This law relates to e.m.f.s and voltage drops in a circuit and is sometimes called voltage law. 

A rise in potential should be considered positive while fall in potential should be considered negative.