Current Divider Rule

The Current Divider Rule is applicable to parallel circuits, in which the current is divided into the number of parallel branches. The current in each branch may have a different value depending on the specification of branch component.

In a parallel circuit, the current has different paths to flow but the voltage across each parallel branch is always equal. So the current divider rule explains how the current is divided among the parallel branch.

Current divider circuit

Let us consider a parallel circuit as shown below, which has two resistors R₁ and R₂ connected across the supply voltage V_s. Let I_T be the total current flowing in the circuit, which has two parallel paths via resistor R₁ and R₂. I_R1 is the current flowing through R₁ and I_R2 is the current flowing through R₂.

By Ohm’s Law, the voltage across the resistors R1 and R2 can be written as

$I_{R1} = \frac{V_s}{R_1} --->(1)$

$I_{R2} = \frac{V_s}{R_2} --->(2)$

At node A, by applying Kirchoff’s Current Law, the total current in the parallel circuit can be written as,

$I_T = I_{R1} + I_{R2}$

$I_T = \frac{V_s}{R_1} + \frac{V_s}{R_2} = V_s(\frac{1}{R_1} + \frac{1}{R_2}) = V_s(\frac{R_1 + R_2}{R_1 . R_2})$

$V_s = I_T(\frac{R_1 . R_2}{R_1 + R_2})$

From equation (1), the current I_R1 through the parallel branch R₁ is obtained as below,

$I_{R1} = \frac{V_s}{R_1} = \frac{I_T}{R_1}(\frac{R_1 . R_2}{R_1 + R_2})$

$I_{R1}= I_T(\frac{R_2}{R_1 + R_2})$

Similarly,from equation (2), the current I_R2 through the parallel branch R₂ is obtained as below,

$I_{R2} = \frac{V_s}{R_2} = \frac{I_T}{R_2}(\frac{R_1 . R_2}{R_1 + R_2})$

$I_{R2}= I_T(\frac{R_1}{R_1 + R_2})$

Solved Problem 1

Consider two parallel resistors 25Ω and 15Ω are connected across the supply voltage of 40 V. Find the current flowing through each resistor and the total current supplied by the source.

In the given problem, R1 = 25 Ω and R2 = 15 Ω, Vs = 40 V.

The current flowing through each resistor is obtained as,

$I_{R1} = \frac{V_s}{R_1} = \frac{40}{25} = 1.6 Amps$