Kirchhoff’s Rules: junction rule, loop rule and sign convention in Kirchhoff's loop rule

 Kirchhoff’s Rules:

 

1) Kirchhoff’s first rule:

also called Junction rule

This rule states that the sum of current entering a junction is equal to the sum of current leaving from the junction.

 

According to this rule

I₁ +   I₂   +  (-I₃)  +  (-I₄)  +  (-I₅)  = 0

Or

I₁ +  I₂  -  I₃  -  I₄  -  I₅  = 0

Here + sign means current enters to the junction

- sign means current leaving from the junction

Therefore

I₁ +  I₂  =  I₃  +  I₄  +  I₅ 

 

 

 

 

2) Kirchhoff’s second law or loop rule

The rule states that

The Algebraic sum of changes in potential around any closed loop or closed path of an electric circuit involving resistors and cells in the loop is zero.

 

 

Now applying Kirchhoff’s rule for the loop ABCFA is

I₁R₁ +  I₁R₂  +  I₃R₃  - e₁   = 0

 

I₁R₁ +  I₁R₂  +  I₃R₃  =  e₁ 

 

e₁  =   I₁R₁ +  I₁R₂  +  I₃R₃ 

 

applying Kirchhoff’s rule for the loop FCDEF is

I₃R₃  +  I₂R₄   -  e₂   = 0

 

I₃R₃  +  I₂R₄   =  e₂  

 

e₂  =   I₃R₃  +  I₂R₄   

 

  

Sign Convention in

Kirchhoff’s loop rule:

 

1) emf of a cell is positive when you moves from positive pole to the negative pole.

2) emf of a cell is negative when you moves from negative pole to the positive pole.

3) the product of current and the resistance of a resistor is positive if the direction of move and the direction of current are same.

4) The product of current and resistance of a resistor is negative if the direction of move is opposite to the direction of current.