Kirchoff's law of current distribution

# Kirchoff's law of current distribution:

1)  First law : The algebraic sum of all electric current meeting at each junction of an electric circuit is zero.

       i.e.  [   ∑ I = 0   ]

For the algebraic sum of current coming towards junction are taken positive and the current going away from the junction are taken negative.

“This law is based on the law of conservation of charge”.

Explain:

For this circuit--

   ∑ I = 0   

i.e.   I1+I2+(-I3)+(-I4)+(-I5) = 0

I1 + I2 - I3 - I4 - I5 = 0

I1 + I2 = I3 + I4 + I5

Thus, the sum of all current coming towards junction is equal to the sum of all current going away from the junction.

2) Second law : According to this law - “In a closed electric circuit the algebraic sum of product of current flowing in different parts and their corresponding resistance and the difference in electro motive force EMF applied in the circuit is zero”.

i.e     {  ∑ I.R + ∑ E = 0  }

“This law is based on the law of conservation of energy”.

For the algebraic sum in the direction of current I.R is taken to be positive while in the direction of opposite to the current it is taken to be negative. 

               Inside the electrolyte of the cell the EMF is taken to be negative from the negative electrode toward the positive electrode while EMF is positive from positive electrode to negative electrode.

Explain:

In a closed circuit ADCBA 

By Kirchoff's second law:

∑ I.R + ∑ E = 0 

[ -I1r1 + I2r2 + E1 - E2 = 0 ]

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