Current Division:

Sometimes it is necessary to search out the individual branch currents in a parallel circuit when just resistance and total current are known.  When only two branches are included, the current in one branch will be a few fraction of I_T.  A resistance in every circuit could be used to divide the total current into fractional currents in every branch. This procedure is known as current division.

I₁ =      R₂/ R₁+R₂ I_T

I₂ =      R₁/ R₁+R₂ I_T                                                                   (2-13)

Note that the equation for every branch current has the opposite R in the numerator. This is since each branch current is inversely proportional to the branch resistance.

Example: Find out branch current for I₁ and I₂ for the circuit display in Figure.

Figure: Current Division Example Circuit

Solution:

I₁ = R₂/ R₁+R₂ I_T =8/6+8 (24) =8/14(24) =13.71 amps

I₂ = R₁/ R₁+R₂ I_T =6/6+8 (24) =6/14(24) =10.29 amps

Since I₁ and I_T were known, we could have also simply subtracted I₁ from I_T to find out I₂:

I_T = I₁ + I₂

I₂ = I_T - I₁

=24- 13.71

=10.29 amps