From the Kirchoffs Current law: The algebraic sum of currents entering the node and the sum of currents leaving the node will be zero.
Therefore when current flowing through the conductor encounters a node current will be split according to the impedance of the circuits. Current division rule applies to resistors which are in parallel. Now consider a figure for explaining current division rule:
In the above circuit current "i" flowing through the circuit splits in to "i1" and "i2" according to the resistor values R1 and R2
Equivalent resistor value for the two resistors in parallel is given by:
Then the Kirchoff's voltage equation will be:
Combining the above two equations current dividing in each branch will be given as:
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