# Calculating Total Resistance In A Series Parallel Circuit

Calculating the total resistance in a series-parallel circuit can be a bit tricky, but it's not impossible. With a little bit of math, you can easily find the total resistance of any series-parallel circuit.

To start, you need to identify the different components in the circuit. In a series-parallel circuit, there will be two or more resistors connected in series, and two or more resistors connected in parallel.

Resistors connected in series are connected end-to-end, so that the same current flows through each resistor. The total resistance of a series circuit is equal to the sum of the individual resistances of the resistors in the circuit.

Resistors connected in parallel are connected across each other, so that the same voltage is applied to each resistor. The total resistance of a parallel circuit is equal to the reciprocal of the sum of the reciprocals of the individual resistances of the resistors in the circuit.

Once you've identified the different components in the circuit, you can start to calculate the total resistance. To do this, you need to first calculate the resistance of each series and parallel section of the circuit. Then, you can add the resistances of the series sections together to find the total resistance of the series portion of the circuit. Finally, you can add the resistance of the parallel sections together to find the total resistance of the parallel portion of the circuit.

For example, consider the following series-parallel circuit:

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

The resistance of the series section is equal to R1 + R2 = 10 + 20 = 30 ohms. The resistance of the parallel section is equal to 1 / (1 / R3 + 1 / R4) = 1 / (1 / 5 + 1 / 10) = 1 / (0.2 + 0.1) = 5 ohms.

Now that we know the resistance of each series and parallel section, we can add them together to find the total resistance of the circuit. The total resistance is equal to 30 + 5 = 35 ohms.

Calculating the total resistance of a series-parallel circuit can be a bit tricky, but it's not impossible. With a little bit of math, you can easily find the total resistance of any series-parallel circuit.

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