In this article, we will discuss how to calculate the total resistance in a series-parallel circuit. We will start by defining what a series-parallel circuit is, and then we will show you how to calculate the total resistance using the following steps:

- Identify the series and parallel components in the circuit.
- Calculate the resistance of each series component.
- Calculate the equivalent resistance of each parallel component.
- Add the equivalent resistances of the parallel components to find the total resistance of the circuit.

Let's take a look at an example. Consider the following series-parallel circuit:

In this circuit, there are two resistors in series (R1 and R2) and two resistors in parallel (R3 and R4). To calculate the total resistance of this circuit, we would first need to calculate the resistance of each series component.

The resistance of a resistor in series is equal to the sum of the resistances of all of the resistors in series. In this case, the resistance of R1 and R2 is equal to R1 + R2 = 10 Ω + 20 Ω = 30 Ω.

Next, we need to calculate the equivalent resistance of each parallel component. The equivalent resistance of a resistor in parallel is equal to the reciprocal of the sum of the reciprocals of all of the resistors in parallel. In this case, the equivalent resistance of R3 and R4 is equal to 1 / (1 / 10 Ω + 1 / 20 Ω) = 5 Ω.

Finally, we can add the equivalent resistances of the parallel components to find the total resistance of the circuit. In this case, the total resistance is equal to 30 Ω + 5 Ω = 35 Ω.

We can verify this result by using the following equation:

where:

* Rtotal is the total resistance of the circuit * R1, R2, R3, and R4 are the resistances of the individual resistors

In this case, we have:

As we can see, the total resistance of the circuit is equal to 35 Ω, which is the same value that we calculated using the series-parallel method.

We hope this article has helped you understand how to calculate the total resistance in a series-parallel circuit. If you have any questions, please feel free to leave a comment below.

Here are some additional resources that you may find helpful:

- Khan Academy: Series and Parallel Circuits
- Physics Classroom: Series and Parallel Circuits
- Electronics Tutorials: Series and Parallel Resistors

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