Current Divider Rule: What is it? Formula, Derivation & Examples

When current source is connected to the circuit elements which are in parallel, the total current flowing in the circuit gets divided in each element according to resistance or impedance of the circuit element. Thus, the current is divided in all the branches. The voltage across each branch element remains the same because these elements are connected in the parallel.


Current Divider Formula Derivation


The current division or current divider rule can be well understood with following explanation.

current divider circuit diagram

The current through R1 and R2 Resistance can be calculated using Ohm’s law;

Current through resistance R1


Current through resistance R1




Current through resistance R2




Total equivalent resistance of the parallel circuit is R




Total current flowing in the circuit is I ;








Putting the value of V in equation (1) we get;

current divider formula








Putting the value of V in equation (2) we get;

current divider formula









Current Divider Formula


Thus, the current in the parallel branch is equal to the ratio of opposite branch resistance to the total resistance multiplied by the total circuit current. The current divider formula is as given below.

general formula of current divider



Illustrative Example on Current Divider:


Two resistances 50Ω and 100Ω is connected in parallel with a current source of 50A. Find the current flow through each resistor.

numerical problem  current  divider circuit diagram




Current through 50 Ω resistance is I1









Current through 100 Ω resistance is I2










Note:

Current divider rule is used when two or more circuit elements are connected in parallel with a current source.


When the two or more circuit elements are connected in parallel with voltage source, the current in the each branch can be calculated by simply applying the Ohm’s law because voltage across each circuit element is the same and by dividing the voltage with branch resistance, the current in the branch can be easily calculated.

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