Electronics Handbook/Circuits/Current Divider

Current Divider
If two elements are in parallel, the voltage across them must be the same, but the current divides according to the resistances. A simple circuit with two (or more) resistors in parallel with a source is called a current divider.


 * [[Image:Resistorsparallel.png]]

Figure B: Parallel Resistors.

Mathmatic Formula
If a voltage V appears across the resistors in Figure B with only $$R_1$$ and $$R_2$$ for the moment then the current flowing in the circuit, before the division, i is according to Ohms Law.
 * $$i=\frac{V}{R_{eq}}$$

Using the equivalent resistance for a parallel combination of resistors is
 * $$i=\frac{V(R_1+R_2)}{R_1R_2}$$          (1)

The current through $$R_1$$ according to Ohms Law is
 * $$i_1=\frac{V}{R_1}$$           (2)

Dividing equation (2) by (1)
 * $$i_1=\frac{iR_2}{R_2+R_1}$$

Similarly
 * $$i_2=\frac{iR_1}{R_2+R_1}$$

In general with n Resistors the current $$i_x$$ is
 * $$i_x=\frac{iR_1R_2\cdots R_n}{ (R_2\cdots R_n+\cdots+ R_1\cdots R_{n-1}) R_x}$$

Or possibly more simply
 * $$\frac{i_x}{i}=\frac{R_{eq}}{R_x}$$

Where
 * $$R_{eq}=\frac{R_1\cdots R_n}{R_2\cdots R_n+\cdots+ R_1\cdots R_{n-1}}$$