Electrical current divider rule

Consider the circuit shown in figure where two resistors are connected parallel. Supplying voltage for current resistor. From Ohm’s law we get

v = i1R1
= i2R2

or i1 = V/R1, i2 = V/R2 …………….. (i)

Applying KCL,
i = i1 + i2

Substituting and adding the value in equation (i) then we get,

i = V/R1+ V/R2
= V (1/R1 + 1/R2)
= V/Req

Here Req is the equivalent resistance.

1/Req = (1/R1) + (1/R2)
Or 1/Req = (R1 + R2)/ R1 R2
Req = R1 R2/ (R1 + R2)

Using current divider rule,

I1= R2i/ (R1 + R2)

I2= R1i/ (R1 + R2)