### CURRENT DIVIDER FORMULA

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Using Ohm’s law, we can derive a formula (called the current divider) that can be used to calculate the current through any branch of a multiple-branch parallel circuit:

where

I_{x} = current to be calculated, in branch x

R_{T}= total resistance

R_{x} = resistance in branch x

I_{T} = total current

Example 1

First, we’ll solve for the currents using Ohm’s Law.

The total resistance:

The voltage:

V = R_{T}*I_{S} = 1.2*5 = 6 V;

and so the currents:

Now let’s see how to use the current divider formula. Although at first glance it looks as though we’re using a different formula from the one given at the beginning of this tutorial, in fact the formula is equivalent for the case of two resistors in parallel. Starting from the formula given earlier, substitute (R1*R2)/(R1+R2) for Rt and simplify to arrive at the formula used below.

The results are the same as those calculated by TINA.

Example 2

Find the current in resistor R1.

Here we have two branches in parallel connected to the current source. One of the branches is a series-parallel circuit. Current division must be used twice: