How To Find Total Resistance In A Parallel Circuit

In this article, we will discuss how to find the total resistance in a parallel circuit. We will start by reviewing the basics of parallel circuits, and then we will show you how to use the formula for total resistance to calculate the resistance of a parallel circuit.

## What is a Parallel Circuit? A parallel circuit is a circuit in which two or more components are connected in parallel. This means that the components are all connected to the same voltage source, but they are not connected to each other.

The following diagram shows a simple parallel circuit with three resistors.

A simple parallel circuit with three resistors.

In this circuit, the three resistors are all connected to the same voltage source, but they are not connected to each other. This means that the current flowing through each resistor is the same, but the voltage drop across each resistor is different.

## Formula for Total Resistance The formula for total resistance in a parallel circuit is:

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

where:

* Rt is the total resistance of the circuit * R1, R2, ..., Rn are the resistances of the individual resistors

To use this formula, you simply need to add the reciprocals of the individual resistances. For example, if you have a circuit with three resistors with resistances of 1 Ω, 2 Ω, and 3 Ω, the total resistance of the circuit would be:

``` Rt = 1 / (1 / 1 Ω + 1 / 2 Ω + 1 / 3 Ω) = 1.5 Ω ```

## Calculating Total Resistance Now that we know the formula for total resistance, let's take a look at how to calculate the total resistance of a parallel circuit.

### Example 1 Let's say we have a circuit with two resistors, R1 and R2, that are connected in parallel. The resistance of R1 is 10 Ω, and the resistance of R2 is 20 Ω. What is the total resistance of the circuit?

To solve this problem, we can use the formula for total resistance:

``` Rt = 1 / (1 / R1 + 1 / R2) ```

In this case, R1 = 10 Ω and R2 = 20 Ω, so we can substitute these values into the formula:

``` Rt = 1 / (1 / 10 Ω + 1 / 20 Ω) = 5 Ω ```

Therefore, the total resistance of the circuit is 5 Ω.

### Example 2 Let's say we have a circuit with three resistors, R1, R2, and R3, that are connected in parallel. The resistance of R1 is 10 Ω, the resistance of R2 is 20 Ω, and the resistance of R3 is 30 Ω. What is the total resistance of the circuit?

To solve this problem, we can use the formula for total resistance:

``` Rt = 1 / (1 / R1 + 1 / R2 + 1 / R3) ```

In this case, R1 = 10 Ω, R2 = 20 Ω, and R3 = 30 Ω, so we can substitute these values into the formula:

``` Rt = 1 / (1 / 10 Ω + 1 / 20 Ω + 1 / 30 Ω) = 6.67 Ω ```

Therefore, the total resistance of the circuit is 6.67 Ω.

## Conclusion In this article, we have discussed the basics of parallel circuits and how to calculate the total resistance of a parallel circuit. We have also provided two examples to illustrate how to use the formula for total resistance.

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