KIRCHOFF's LAWS

Kirchoff’s Laws :

1st Law / Junction Rule: 

Across any junction algebric sum of all currents is zero; This is a consequence of Conservation of charge principle.

2nd Law / Loop Rule:

This is a consequence of conservation of energy principle. Across any loop i.e. closed path work done by all agents is equal to zero. this follows from the fact that in  a circuit the drift speed of electrons remains constant.

           

Following convention can be used to apply Kirchoff’s law    

       

Illustration 1.    A battery of  emf 2.0 volts and internal resistance  is being charged with a current of 5.0 A. What is the potential difference between the terminals of the battery 

Solution :          As the battery is being charged, the current goes into the positive terminal as shown in the figure. The potential drop across the internal resistance is

                                     

 Hence, the potential drop across the terminals will be

                                                              

Illustration 2.    Determine the current in each branch of the network shown in the figure

Solution :      

   Each branch of the network is assigned an unknown current to be determined by the application of Kirchhoff’s

rules. To reduce the number of unknowns at the outset, the first rule of the Kirchoff’s is used at every junction

to assign the unknonw current in each branch. We then have three unknown current in each branch. We then

have three unknowns which can be found by applying the second rule of Kirchhoff to three different

closed loops. Kirchhoff’s second rule for the closed loop ADCA gives, 

that is,  

For the closed loop ABCA, we get 

that is,

For the closed loop BCDEB, 

.

we get 

For the closed loop BCDEB, we get  

 that is 

Equations are three simultaneous equations in three unknowns. These can be solved by the ususal method to give            

               

The currents in the various branches of the network are

 

It is easily verfied that Kirchhoff’s second rule applied to the remaining closed loops does not provide any

additonal independent equation, that is, the above values of currents satisfy the second rule for every closed

loop of the network. For example, the total voltage drop over the closed loop BADEB.

is equal to zero, as required by Kirchhoff’s second rule.