# How To Calculate The Total Resistance Of A Series Parallel Circuit

A series-parallel circuit is a circuit that contains both series and parallel connections. To calculate the total resistance of a series-parallel circuit, you can use the following steps: 1.

### Calculate the resistance of each series circuit.

To do this, add the resistances of the resistors in each series circuit together. 2.

### Calculate the equivalent resistance of each parallel circuit.

To do this, divide the sum of the reciprocals of the resistances of the resistors in each parallel circuit by the number of resistors in the parallel circuit. 3.

### Add the equivalent resistances of the parallel circuits together.

This will give you the total resistance of the series-parallel circuit. Here is an example of a series-parallel circuit:

In this circuit, there are two series circuits: one with resistors R1 and R2, and one with resistors R3 and R4. The two series circuits are connected in parallel. To calculate the total resistance of this circuit, we first need to calculate the resistance of each series circuit. The resistance of the first series circuit is R1 + R2 = 10 Ω + 20 Ω = 30 Ω. The resistance of the second series circuit is R3 + R4 = 40 Ω + 50 Ω = 90 Ω. We then need to calculate the equivalent resistance of each parallel circuit. The equivalent resistance of the first parallel circuit is 1 / (1 / 30 Ω + 1 / 90 Ω) = 15 Ω. The equivalent resistance of the second parallel circuit is 1 / (1 / 40 Ω + 1 / 50 Ω) = 25 Ω. Finally, we add the equivalent resistances of the parallel circuits together to get the total resistance of the circuit: 15 Ω + 25 Ω = 40 Ω.

The total resistance of a series-parallel circuit can also be calculated using the following formula:

R = (R1R2 + R3R4) / (R1 + R2 + R3 + R4)

where R is the total resistance of the circuit, R1, R2, R3, and R4 are the resistances of the resistors in each series circuit, and R1 + R2 + R3 + R4 is the sum of the resistances of all of the resistors in the circuit.

In the example above, the total resistance of the circuit can be calculated using the following formula:

R = (30 Ω * 90 Ω + 40 Ω * 50 Ω) / (30 Ω + 90 Ω + 40 Ω + 50 Ω) = 40 Ω

This is the same answer that we got using the method of calculating the resistance of each series circuit and then adding the equivalent resistances of the parallel circuits together.

Calculating the total resistance of a series-parallel circuit can be a bit tricky, but it is a necessary skill for anyone who works with electrical circuits. By following the steps in this article, you will be able to calculate the total resistance of any series-parallel circuit.

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