Parallel electrical circuits, the current doesn’t remain the same. The current divider rule(CDR) is used to find the divided current in parallel circuits.

Table of Contents

**Statement of Current Divider rule:**

**Statement : The electrical current entering the node of a parallel circuit is divided into the branches. Current divider formula is engaged to calculate the magnitude of divided current in the circuits.**

#### Current Divider Formula:

A common formula for the current *I _{X}* in a resistor

*R*that is in parallel with a combination of other resistors of total resistance

_{X}*R*is :

_{T}

Where *I _{T}* is the total current entered into the network of

*R*in parallel with

_{X}*R*. when

_{T}*R*is composed of a parallel combination of resistors, say

_{T}*R*,

_{1}*R*, …… then the mutual of each resistor must be added to find the total resistance

_{2}*R*:

_{T}Fig:1

#### Derivation:

A normal circuit with two resistors in parallel with a voltage source is called a current divider.

The current I has been divided into I_{1 }and I_{2} into two parallel branches with the resistance R_{1 }and R_{2} and V is the voltage drop across the resistance R_{1} and R_{2}.

As we know

V = IR ……..(1)

Equation of the current is written as,

Let the total resistance of the circuit be R and is given by the equation shown below,

Equation (1) can also be written as

I = V/R ……….(3)

Now, putting the value of R from the equation (2) in the equation (3) we will get

here,

Putting the value of V = I_{1}R_{1} from the equation (5) in the equation (4), we finally get the equation as

And now considering V = I_{2}R_{2} the equation will be,

Thus, from the equation (6) and (7) the value of the current I_{1} and I_{2}respectively is given by the equation below,

Thus, In the current division rule, It is said that the current in any of the parallel branches is equal to the proportion of opposite branch resistance to the total resistance, multiplied by the total current.

#### Example of Current Divider:

An electrical circuit has two parallel resistors of 2 ohms and 10 ohms. Apply the current divider equation to find the current flowing through both resistors when the input is 5 Ampere.

**Solution:**

Similarly, we can solve the three parallel resistors.

## 11 comments

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Thanks for the nice explantion ! There is however a small mistake in equation 7. It says I = I1*R1/(R1+R1) where it should say I = I2*…

Anyways, well done!

Off course, the division and multiplication should be switched in my comment, but you get the point!

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May i apply this rule if circuit contains capacitor and resistor both.

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