In this article, we will discuss how to find the total resistance in a series-parallel circuit. We will start by defining what a series-parallel circuit is, and then we will walk through the steps on how to find the total resistance. Finally, we will provide some examples of series-parallel circuits and show how to calculate the total resistance in each case.

A series-parallel circuit is a circuit that contains both series and parallel connections. In a series connection, the components are connected end-to-end, so that the current flows through each component in turn. In a parallel connection, the components are connected across each other, so that the current can flow through any of the components.

To find the total resistance in a series-parallel circuit, we can use the following formula:

``` Rtotal = R1 + R2 + ... + Rn ```

where R1, R2, ..., Rn are the resistances of the individual components in the circuit.

To illustrate how to use this formula, let's consider the following circuit:

In this circuit, we have two resistors in series (R1 and R2) and two resistors in parallel (R3 and R4). To find the total resistance, we can first find the resistance of the series resistors:

``` R1 + R2 = 10 Ω + 20 Ω = 30 Ω ```

Then, we can find the resistance of the parallel resistors:

``` 1 / R3 + 1 / R4 = 1 / 10 Ω + 1 / 20 Ω = 1 / 6 Ω ```

Finally, we can add the resistances of the series and parallel resistors to find the total resistance:

``` Rtotal = 30 Ω + 1 / 6 Ω = 36 Ω ```

As you can see, the total resistance of a series-parallel circuit is simply the sum of the resistances of the individual components.

Here are some additional examples of series-parallel circuits and how to calculate the total resistance:

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### Example 1:

A circuit with two resistors in series (R1 = 10 Ω and R2 = 20 Ω) and two resistors in parallel (R3 = 10 Ω and R4 = 20 Ω).The total resistance of the series resistors is 30 Ω, and the total resistance of the parallel resistors is 1 / 6 Ω. Therefore, the total resistance of the circuit is 36 Ω.

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### Example 2:

A circuit with three resistors in series (R1 = 10 Ω, R2 = 20 Ω, and R3 = 30 Ω).The total resistance of the series resistors is 60 Ω.

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### Example 3:

A circuit with three resistors in parallel (R1 = 10 Ω, R2 = 20 Ω, and R3 = 30 Ω).The total resistance of the parallel resistors is 6 Ω.

I hope this article has helped you to understand how to find the total resistance in a series-parallel circuit. If you have any questions, please feel free to ask in the comments below.

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