Contents

## SI Prefixes

You should know these. If you don’t, you need to learn them.

Prefix | Symbol | Value | |
---|---|---|---|

pico– | p | 10^{−12} |
= 0.000 000 000 001 |

nano– | n | 10^{−9} |
= 0.000 000 001 |

micro– | µ | 10^{−6} |
= 0.000 001 |

milli– | m | 10^{−3} |
= 0.001 |

kilo– | k | 10^{3} |
= 1 000 |

mega– | M | 10^{6} |
= 1 000 000 |

giga– | G | 10^{9} |
= 1 000 000 000 |

tera– | T | 10^{12} |
= 1 000 000 000 000 |

## Resistors in Series

The formula for calculating the total resistance for resistors in series is fairly straightforward.

**R _{total} = R_{1} + R_{2} + R_{3} + … + R_{n}**

For example, if you have three resistors with values 330 Ω, 47 kΩ, and 1 kΩ, you can calculate R_{total} like this:

R_{total} = 330 Ω + 47000 Ω + 1000 Ω = 48330 Ω or 48.33 kΩ

## Resistors in Parallel

The formula for calculating the total resistance for resistors in parallel is a little more complicated.

**1 / R _{total} = 1 / R_{1} + 1 / R_{2} + … + 1 / R_{n}**

Step 1: We need to clear all the fractions by multiplying by the lowest common denominator, which is (R_{total} × R_{1} × R_{2}). Multiplying both sides by the lowest common denominator, we get

(R_{total} × R_{1} × R_{2}) × (1 / R_{total}) = (1 / R_{1} + 1 / R_{2}) × (R_{total} × R_{1} × R_{2})

Step 2: Using the distributive property (I bet you wish you had paid attention in math class), we get

(R_{total} × R_{1} × R_{2}) / R_{total} = (R_{total} × R_{1} × R_{2}) / R_{1} + (R_{total} × R_{1} × R_{2}) / R_{2}

Step 3: Simplifying the equation, we get

(~~R~~ × R_{total}_{1} × R_{2}) / ~~R~~ = (R_{total}_{total} × ~~R~~ × R_{1}_{2}) / ~~R~~ + (R_{1}_{total} × R_{1} × ~~R~~) / _{2}~~R~~_{2}

Which is the same as

R_{1} × R_{2} = R_{total} × R_{2} + R_{total} × R_{1}

Step 4: Collecting all the R_{1} terms on the left side of the equal sign we get

R_{1} × R_{2} − R_{total} × R_{1} = R_{total} × R_{2}

Which is the same as

R_{1} × (R_{2} − R_{total}) = R_{total} × R_{2}

Step 5: Dividing both sides by (R_{2} − R_{total}) we get

R_{1} = (R_{2} × R_{total}) / (R_{2} − R_{total})

Using the same method we get

R_{2} = (R_{1} × R_{total}) / (R_{1} − R_{total})

Step 6: Back at step 3 we had

R_{1} × R_{2} = R_{total} × R_{2} + R_{total} × R_{1}

Using the distributive property, we get

R_{1} × R_{2} = R_{total} × (R_{2} + R_{1})

Step 7: Divide both sides by (R_{2} + R_{1}) and we get

(R_{1} × R_{2}) / (R_{2} + R_{1}) = R_{total}

Which is the same as

R_{total} = (R_{1} × R_{2}) / (R_{1} + R_{2})

So when we have a circuit with two resistors in parallel, our three formulas for calculating the values of R_{1}, R_{2}, or R_{total} when we have two of the three values are

**R _{total} = (R_{1} × R_{2}) / (R_{1} + R_{2})**

**R _{1} = (R_{2} × R_{total}) / (R_{2} − R_{total})**

**R _{2} = (R_{1} × R_{total}) / (R_{1} − R_{total})**

That is a lot of work to do by hand. Fortunately, we have the computer do the work for us. In the next section we have a parallel resistance calculator for circuits with two parallel resistors.

## Parallel Resistance Calculator for Two Resistors

To use the calculator, enter a resistor value in two of the three boxes. The third value of the parallel circuit will be calculated.

For example, you could enter values for R_{1} and R_{2} and have R_{total} calculated. Or you could enter R_{total} and R_{1} and have R_{2} calculated. Or you could enter R_{total} and R_{2} and have R_{1} calculated.

The drop-down list allows you to set the unit of measurement for R_{1}, R_{2}, and R_{total}. You can choose µΩ (microohm), mΩ (milliohm), Ω (ohm), kΩ (kiloohm), or MΩ (megaohm).

## Parallel Resistance Calculator for Up to 10 Resistors

*Coming soon…*