CURRENT DIVIDER RULE

CURRENT DIVIDER RULE

Resistors in series, receive the same current flow in a circuit from a voltage source. For example in figure 1 bellow;

Figure 1

R₁ and R₂ and in series and the same current I is passing through them.

we can deduce that; 

R_T= R₁ +R₂ (resultant of resistors in series)

Conversely, for resistors connected in parallel, they share the current flow depending on their resistance value. Note that current tends to flow towards path of least resistance.

Let’s buttress this further with example in figure 2.

Figure 2

In figure 2, R₁||R₂, current I, is divided at the node and I₁ flows into R₁ and I₂ into R₂

That is, I = I₁ +I₂.

The circuit in figure 2a can be redrawn and represented with the circuit in figure 2b, as R_T is resultant resistance of R₁ and R₂ in the circuit.

We can see that;  V_in = IR_T

Remember that V_in = V_R1= V_R2 (voltage in parallel) SeeVOLTAGE DIVIDER 

Also that;

        

 ....................(1a)

likewise for I₂,

......................(1b)

1a and 1b is known as Current divider rule.