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 of finding the total resistance. We will also provide some examples to help you understand the process.

A series-parallel circuit is a circuit that contains both series and parallel connections. In a series connection, the components are connected in a single path, so that the current flows through all of the components in the same order. In a parallel connection, the components are connected in separate paths, so that the current can flow through any of the components.

To find the total resistance in a series-parallel circuit, we need to first find the equivalent resistance of each of the series and parallel sections. The equivalent resistance of a series connection is the sum of the individual resistances, and the equivalent resistance of a parallel connection is the reciprocal of the sum of the reciprocals of the individual resistances.

Once we have found the equivalent resistance of each of the series and parallel sections, we can add them together to find the total resistance of the circuit.

Here is an example of a series-parallel circuit:

In this circuit, the resistors R1, R2, and R3 are connected in series, and the resistors R4 and R5 are connected in parallel. To find the total resistance of this circuit, we first need to find the equivalent resistance of the series connection:

R1 + R2 + R3 = 10 Ω + 20 Ω + 30 Ω = 60 Ω

Once we have found the equivalent resistance of the series connection, we can find the equivalent resistance of the parallel connection:

1 / (1 / 40 Ω + 1 / 60 Ω) = 24 Ω

Now that we have found the equivalent resistance of each of the series and parallel sections, we can add them together to find the total resistance of the circuit:

24 Ω + 60 Ω = 84 Ω

Therefore, the total resistance of this circuit is 84 Ω.

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

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