Kirchoff's Law, Mesh and Nodal annalysis

Kirchoff's Law:

      Only Ohm's Law unable to gives  current in a complicated circuits. In 1845, a German physicist, Gustav Kirchhoff developed a pair or set of rules or laws which deal with the conservation of current and energy within electrical circuits. These law are 

              (i) Kirchoff's Point Law of Kirchiff's Current Law

              (ii)  Kirchoff's Mesh Law of Kirchiff's Voltage Law

 (i) Kirchoff's Point Law of Kirchiff's Current Law:

                It state that , In any electrical network, the algebraic sum of the currents meeting at a point or junction is zero

Assuming all in coming current as a positive and all outgoing current as a negative.we have            
                          I1 + I2 –  I3 – I4 – I5 = 0
                          I1 + I2 =  I3 + I4 + I5 
                           Incoming currents = Outgoing currents

(ii)  Kirchoff's Mesh Law of Kirchiff's Voltage Law:

                      It state that, The algebraic sum of  products of currents resistances in each of the conductors in any closed path or mesh in a network plus the algebraic sum of the e.m.fs in that path is zero. 

   

                                IR1 + IR2 + IR3 – E = 0
                                 i.e,    Σ IR +  Σ E = 0