current divider (thing)

A current divider is a quick way to determine the current flowing through a resistor. The result you get will be the same as if you used Kirchhoff's Laws, but using the current divider will help you save time. Like the voltage divider, the current divider is just a time saving trick that comes from patterns in solving similar circuits.

When there are two resistors in parallel, the current going through one resistor is equal to the current coming in to both of them, times the other resistor's resistance, divided by the sum of the two resistances. Let's look at an example:

    
    ---------------------------
    |             |           |
    |             |           |
   / \            /           /
  /  ^\ I:        \  R1:      \  R2:
 | 1A| |1 Ampere  /  2 Ohm    /  5 Ohm
  \  |/ current   \  resistor \  resistor
   \ /  source    |           |
    |             |           |
    |             |           |
    ---------------------------
                  |
                  |
                -----
                 ---   Ground
                  -

Using the relation described above, the current through R1 would be equal to (I * R2)/(R1 + R2), or 2/7. The current through R2 would be (I * R1)/(R1 + R2), or 5/7. Does this check out if we use Kirchhoff's Laws?

Current through R1 = i1
Current through R2 = i2
Voltage at non-grounded node: V

I = i1 + i2 (Kirchhoff's Current Law)
V = i1 * R1 (Ohm's Law)
V = i2 * R2 (Ohm's Law)

Equation manipulation:
I = i1 + (V / R2)
I = i1 + ((i1* R1) / R2)
R2 * I = (i1 * R2) + (i1 * R2)
R2 * I = i1 * (R1 + R2)
i1 = (R2 * I) / (R1 + R2), exactly what was given by the current divider relation.

It's cumbersome to have to do that math each time we see resistors in parallel. So, we can just memorize the current divider relation and circuit analysis becomes that much easier.