Current Divider Rule Example # 2: A Difficult CDR Example with Rt 20 ohms given

In this example you'll learn the application of current divider principle to a circuit whose equivalent resistance and one of the two resistors are known.

Statement: A current divider circuit has two resistors with R1 = 30 ohms and R2 is unknown. While the equivalent resistance is 20 ohms. The current flowing through R2 is 2 mA.

By appliying current divider theorem to I1, we obtain.

I₁ = (20 ohm/ 30 ohm) * I_t

or I₁ = 0.666 I_t

From Kirchhoff's Current Law:

I_t = I₁ + I₂

or

I_t = 0.66 I_t + I₂

0.33 I_t = I₂/

0.33 I_t = 2 mA

or I_t = 6 mA

Putting value of I_t in I₁.
I₁ = 3.99 mA