Current divider rule at a node with 2 resistor branches

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CURRENT DIVIDER RULE

Current divider rule is in the dual position of the voltage divider rule. Current divider rule is applied when a current is supplied to a node formed by two (or multiple) parallel resistors, and a current flowing through a resistor is sought. You can say that the current into the node is divided (or distributed) into two resistor branches, and the sum of two currents at the other node must be the same as the entering current at the node. How much current is flowing through a resistor is what the current divider rule is all about. What it says is that the amount of the current (or the portion of the supplying current) flowing a resistor is inversely proportional to the value of the resistor. After all, according to the Ohm's Law, when voltage is the same, current is inversely proportional to resistance, I=V/R.

If a resistor's value is 20% of the total combined (algebraic sum, not the equivalent resistance of the two parallel resistors) resistance, then the current through the resistor is 80% of the supplied current.The other resistor's value is 80% (100%-20%) and the current through the other resistor is 20% of the applied current.

Consider a resistor of 20W and the other resistor of 30W connected in parallel and a current of 100A is entering from one end of the parallel resistors. The current through 20W is then [30/(20+30)]of the 100A, which is 60A. The current through 30W is [20/(20+30)] of 100A, which is 40A.So the formula can be said: When a current is applied into an end of two parallel connected resistors, the current through a resistor is determined by the portion of the applied current which is calculated by dividing the other resistance by the sum of its resistance and the other resistance of the resistors.

Warning: Apply this current divider rule only when a current (whether a current source or flown by other means) is applied to an end of two resistors connected in parallel. Once you calculate the current through a resistor, you can get the other current also by applying KCL at the node where the applied current is entering.

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