**Two or more resistors are said to be in parallel, if identical voltage is across all the resistors.**

In accordance to Kirhhoff’s Law the current ${I}_{S}={I}_{1}+{I}_{2}+...+{I}_{N}$, and ${V}_{1}={V}_{2}=...={V}_{N}$$=V$.

Here ${I}_{1}=\frac{V}{{R}_{1}},{I}_{2}=\frac{V}{{R}_{2}},...{I}_{N}=\frac{V}{{R}_{N}}$. So ${I}_{S}=V(\frac{1}{{R}_{1}}+\frac{1}{{R}_{2}}+...\frac{1}{{R}_{N}})=\frac{V}{{R}_{eq}}$.

Here parallel resistors can be replaced by the equivalent resistance $\frac{1}{{R}_{eq}}=\frac{1}{{R}_{1}}+\frac{1}{{R}_{2}}+...\frac{1}{{R}_{N}}$, and ${R}_{eq}=\frac{1}{{\displaystyle \frac{1}{{R}_{1}}}+{\displaystyle \frac{1}{{R}_{2}}}+...{\displaystyle \frac{1}{{R}_{N}}}}$.

Then current through a resistor in parallel circuit is ${I}_{n}=\frac{{\displaystyle \frac{1}{{R}_{n}}}}{{\displaystyle \frac{1}{{R}_{1}}}+{\displaystyle \frac{1}{{R}_{2}}}+...{\displaystyle \frac{1}{{R}_{N}}}}{I}_{S}$. This equation is called *current divider*. Current divider is a linear circuit, producing output current equal to a fraction of the input current.

For example, if ${R}_{1}=1$Ohm, ${R}_{2}=2$ Ohm, ${R}_{3}=4$Ohm, ${R}_{4}=2$Ohm and ${I}_{s}=4$A, then ${I}_{3}=\frac{4}{9}$A.