This law is also called Kirchhoff 's loop rule. It is a consequence of the principle of conservation of energy. It states that " The algebraic sum of the potential differences around a circuit must be zero".
Considering that electric potential is defined as line integral of electric field, Kirchhoff's voltage law can be expressed equivalently with equation
For more information on this topic see the below links :
www.wisc-online.com/objects/index.asp?objID=DCE3002 --- online example
www.wisc-online.com/objects/index.asp?objID=DCE5303 ---- Practice Problems