# Parallel Circuit Reciprocal Formula

The parallel circuit reciprocal formula is a mathematical equation that can be used to calculate the total resistance of a parallel circuit. The formula is given by:

``` 1 / Rt = 1 / R1 + 1 / R2 + ... + 1 / Rn ```

where:

*

### Rt

is the total resistance of the parallel circuit *

,

, ...,

### Rn

are the individual resistances of the resistors in the parallel circuit

To use the parallel circuit reciprocal formula, simply add the reciprocals of the individual resistances to find the total resistance. For example, if you have a parallel circuit with three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms, the total resistance of the circuit would be:

``` 1 / Rt = 1 / 10 + 1 / 20 + 1 / 30 ```

``` 1 / Rt = 6 / 60 ```

``` Rt = 60 / 6 = 10 ohms ```

As you can see, the total resistance of the parallel circuit is less than the resistance of any of the individual resistors. This is because the current can flow through multiple paths in a parallel circuit, which reduces the overall resistance.

The parallel circuit reciprocal formula is a useful tool for calculating the total resistance of a parallel circuit. It can be used to design circuits that have a desired resistance, or to troubleshoot circuits that are not working properly.

* [Parallel Circuits](https://www.khanacademy.org/science/physics/electricity-and-magnetism/circuits/a/parallel-circuits) - Khan Academy * [Parallel Circuits](https://www.physicsclassroom.com/class/circuits/Lesson-1/Parallel-Circuits) - Physics Classroom * [Parallel Circuits](https://www.sparkfun.com/tutorials/118) - SparkFun Electronics

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