Let us discuss current division rule
This rule is very important, and widely used in the field of electric engineering
Actually, this rule finds application, when we have to find the current passing through
each impedance when, these are connected in parallel. Let us say, two impedances, Z1, and Z2, are connected in parallel
A current, I, passes through the system. This, I, is then divided into I1, and I2, at this junction
I1, and I2 pass through Z1, and Z2 respectively. Our aim is to determine, I1, and I2 in terms of, I, Z1, and Z2
As, Z1, and Z2 are connected in parallel, voltage drop across each will be, same
Hence, we can write, I1 into Z1 equal to, I2 into Z2, and this is voltage drop across, Z1, or Z2
As total current, I, is divided into I1, and I2, we can write, I, equals to I1, plus, I2
Say, this equation is 2. From, equation 1, we get, I2 equals to, I1 Z1 divided by Z2
Computing, this expression of I2 in equation 2, we get, I, equals to I1, plus, I1 into Z1 divided by, Z2
It implies, I, Z2 equals to I1, Z2, plus I1, Z1, equals to I1 into, Z2 plus Z1
Therefore, I1 equals I, Z2 divided by Z1 plus Z2. Similarly, we can show, I2 equals I, Z1 divided by Z1 plus Z2
From, these expressions of current, we can conclude that, current in any of the parallel paths, is
total current into impedance of the path through which the current is not determined, divided by sum of impedance of parallel paths
Hope you got a basic idea. Thank you