Current Division

The Current Divider Rule

Current divider rule is used to find the current passing through an element connected in a parallel network.

If there are N resistors R₁, R₂,..….R_N; connected in parallel with a source delivering a total current, I_T to the circuit as shown in the below figure. Then the current through i th resistor
R_i is,

I_Ri = I_TR_p/(R_i + R_p).

Where R_p is the equivalent resistance of all the resistors connected in parallel to the resistor R_i excluding R_i.

Resistors connected in parallel

For example, for finding current through a resistor R₁,

I_R1 = I_TR_p/( R₁ + R_p)

Where R_p = 1/(R₂^-1+R₃^-1+….R_N^-1)

Current division for two resistors in Parallel

two resistors connected in parallel

If two resistors R₁ and R₂ are connected in parallel and I_T is the total current delivered by the source then the current through the resistor R₁ is I_R1 = I_TR₂/(R₁+R₂)

Similarly the current through the resistor R₂ is I_R2 = I_TR₁/(R₁+R₂)

Current division for three resistors in Parallel

If there are three resistor R₁, R₂ and R₃ are connected in parallel with a source delivering a current I_T then the current through a the resistor R₂ can be found as below.

I_R2 = [I_T(R₁R₃)/(R₁+R₃)] / [R₂ + {(R₁R₃)/(R₁+R₃)}]

Three resistors connected in parallel

The current division rule can be applied to find the current through an element in an AC network having impedances by using the below formula,

I_Zi = I_TZ_p/(Z_i + Z_p).

Also Read:

Voltage division
Resistors in parallel
Kirchhoff's current law