A series-parallel circuit is a circuit that contains both series and parallel connections. In a series circuit, the current flows through each component in the same path. In a parallel circuit, the current can flow through multiple paths.

Series-parallel circuits can be used to combine the advantages of both series and parallel circuits. For example, a series-parallel circuit can provide more resistance than a simple series circuit, but it can also provide more current than a simple parallel circuit.

The following is an example of a series-parallel circuit:

In this circuit, the resistors R1 and R2 are connected in series, and the combination of R1 and R2 is connected in parallel with the resistor R3.

The total resistance of this circuit can be calculated using the following formula:

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

Where:

* Rt is the total resistance of the circuit * R1 is the resistance of resistor R1 * R2 is the resistance of resistor R2

In this example, the total resistance of the circuit is:

``` Rt = 10 Ω + 20 Ω + (10 Ω * 20 Ω) / (10 Ω + 20 Ω) = 50 Ω ```

The following is a table of sample problems with answers for series-parallel circuits:

| Problem | Answer | |---|---| | What is the total resistance of a circuit with two resistors in series, R1 = 10 Ω and R2 = 20 Ω? | 30 Ω | | What is the total resistance of a circuit with two resistors in parallel, R1 = 10 Ω and R2 = 20 Ω? | 5 Ω | | What is the total resistance of a circuit with three resistors in series, R1 = 10 Ω, R2 = 20 Ω, and R3 = 30 Ω? | 60 Ω | | What is the total resistance of a circuit with three resistors in parallel, R1 = 10 Ω, R2 = 20 Ω, and R3 = 30 Ω? | 6 Ω |

I hope this article has been helpful in understanding series-parallel circuits. If you have any questions, please feel free to ask in the comments section below.

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