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.

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

$i={\frac {V(R_{1}+R_{2})}{R_{1}R_{2}}}$ (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

$i_{x}={\frac {iR_{1}R_{2}\cdots R_{n}}{(R_{2}\cdots R_{n}+\cdots +R_{1}\cdots R_{n-1})R_{x}}}$

Or possibly more simply

${\frac {i_{x}}{i}}={\frac {R_{eq}}{R_{x}}}$

Where

$R_{eq}={\frac {R_{1}\cdots R_{n}}{R_{2}\cdots R_{n}+\cdots +R_{1}\cdots R_{n-1}}}$