In this lesson, you will create a smaller current from a bigger current with parallel resistors.

## Voltage and parallel resistors

When two resistors, R1 and R2, are connected in parallel, the voltages across the resistors are identical.

$V = V_{1} = V_{2}$

## Current and parallel resistors

Each current thorough a resistor is:

$I_{1} = { V_{1} \over R_{1} } = { V \over R_{1} }$ $I_{2} = { V_{2} \over R_{2} } = { V \over R_{2} }$

For example, when $V = 10 V$, $R_{1} = 10 ohm$, and $R_{2} = 20 ohm$,

$I_{1} = { V \over R_{1} } = { 10 V \over 10 ohm } = 1 (A)$ $I_{2} = { V \over R_{2} } = { 10 V \over 20 ohm } = 0.5 (A)$

When $R_{1} = R_{2}$, the same amount of current flows.

$I_{1} = { V_{1} \over R_{1} } = { V \over R_{1} }$ $I_{2} = { V_{2} \over R_{2} } = { V \over R_{1} }$ $I_{1} = I_{2}$

The total current is:

$I_{total} = I_{1} + I_{2} = { V \over R_{1} } + { V \over R_{2} }$ $I_{total} = I_{1} + I_{2} = 1 A + 0.5 A = 1.5 (A)$

## Resistance and parallel resistors

The total resistance is:

$R_{total} = { V \over I } = { V \over I_{total} } = { V \over { { V \over R_{1} } + { V \over R_{2} } } }$ ${ R_{total} } = { 1 \over { 1 \over R_{1} } + { 1 \over R_{2} } }$ ${ R_{total} } = { V \over I_{total} } = { 1 \over { 1 \over 10 ohm } + { 1 \over 20 ohm } } = { 10 \over 1.5 } \approx 6.666 (ohm)$

## Quick formulas

With $N$ resistors:

${ R_{total} } = { 1 \over { 1 \over R_{1} } + { 1 \over R_{2} } + \dots + { 1 \over R_{N} } }$

With two resistors:

$R_{total} = { 1 \over { 1 \over R_{1} } + { 1 \over R_{2} } } = { { R_{1} \times R_{2} } \over { R_{1} + R_{2} } }$

## Other lessons

Other lessons in Electronics Basic Course: