How To Find Total Resistance In Series Parallel Circuit

By | September 19, 2023



When it comes to understanding electrical circuits, one of the most important concepts to grasp is the concept of resistance. Resistance is the measure of how much a material or component hinders the flow of electricity. In a series parallel circuit, where there are multiple resistors connected in both series and parallel, finding the total resistance can seem like a daunting task. But fear not, as we break down the steps to easily find the total resistance in a series parallel circuit.

To begin, let's first define what a series parallel circuit is. In simple terms, it is a combination of both series and parallel circuits. In a series circuit, the components are connected end to end, meaning that the current has only one path to flow through. In a parallel circuit, the components are connected side by side, providing multiple paths for the current to flow through. In a series parallel circuit, there are sections of the circuit that are connected in series and others that are connected in parallel.

Now, to find the total resistance in a series parallel circuit, we must first identify which resistors are connected in series and which are connected in parallel. This can be done by following the path of the current and identifying where the components are connected. Once this is determined, we can use the following formula to calculate the total resistance in a series parallel circuit:

1/Rtotal = 1/R1 + 1/R2 + 1/R3...

This formula states that the reciprocal of the total resistance is equal to the sum of the reciprocals of each individual resistor. This may seem complex, but it is actually quite simple to use. Let's take an example: if we have three resistors, R1, R2, and R3, connected in series, with values of 2Ω, 4Ω, and 6Ω respectively, the total resistance would be:

1/Rtotal = 1/2 + 1/4 + 1/6 = 11/12

Therefore, Rtotal = 12/11 Ω

Next, if we have two resistors, R4 and R5, connected in parallel with values of 8Ω and 12Ω respectively, the total resistance would be:

1/Rtotal = 1/8 + 1/12 = 5/24

Therefore, Rtotal = 24/5 Ω

Finally, to find the total resistance of the entire circuit, we can use the same formula again, substituting the calculated values for Rtotal1 and Rtotal2:

1/Rtotal = 1/(12/11) + 1/(24/5)

1/Rtotal = 11/12 + 5/24 = 47/48

Therefore, Rtotal = 48/47 Ω

In conclusion, finding the total resistance in a series parallel circuit may seem daunting, but by understanding the concept and using the appropriate formula, it can be easily calculated. By following the path of the current and identifying which components are connected in series and parallel, we can effectively use the reciprocal formula to find the total resistance. So the next time you encounter a series parallel circuit, don't be intimidated – you now have the knowledge to easily find the total resistance.


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