How To Find Total Resistance In A Series Parallel Circuit

# How to Find Total Resistance in a Series-Parallel Circuit

A series-parallel circuit is a combination of two or more simple circuits connected in series and parallel. To find the total resistance of a series-parallel circuit, you can use the following steps: 1. Find the equivalent resistance of each series circuit. 2. Find the equivalent resistance of each parallel circuit. 3. Add the equivalent resistances of the series and parallel circuits to find the total resistance. Let's look at an example. Consider the following series-parallel circuit:

The first step is to find the equivalent resistance of each series circuit. The first series circuit consists of resistors R1 and R2. The equivalent resistance of a series circuit is equal to the sum of the resistances of the individual resistors. So, the equivalent resistance of the first series circuit is R1 + R2 = 5 Ω + 10 Ω = 15 Ω. The second series circuit consists of resistors R3 and R4. The equivalent resistance of the second series circuit is also 15 Ω. Now that we know the equivalent resistance of each series circuit, we can find the equivalent resistance of the parallel circuits. The equivalent resistance of a parallel circuit is equal to the reciprocal of the sum of the reciprocals of the individual resistances. So, the equivalent resistance of the first parallel circuit is 1 / (1 / 15 Ω + 1 / 15 Ω) = 7.5 Ω. The equivalent resistance of the second parallel circuit is also 7.5 Ω. Finally, we can add the equivalent resistances of the series and parallel circuits to find the total resistance. The total resistance is 15 Ω + 7.5 Ω + 7.5 Ω = 30 Ω. Here is a step-by-step solution to the problem: 1. Find the equivalent resistance of each series circuit. * First series circuit: R1 + R2 = 5 Ω + 10 Ω = 15 Ω * Second series circuit: R3 + R4 = 15 Ω 2. Find the equivalent resistance of each parallel circuit. * First parallel circuit: 1 / (1 / 15 Ω + 1 / 15 Ω) = 7.5 Ω * Second parallel circuit: 1 / (1 / 15 Ω + 1 / 15 Ω) = 7.5 Ω 3. Add the equivalent resistances of the series and parallel circuits to find the total resistance. * Total resistance = 15 Ω + 7.5 Ω + 7.5 Ω = 30 Ω ### Conclusion In this article, we have shown how to find the total resistance of a series-parallel circuit. We used a step-by-step solution to solve a problem involving a series-parallel circuit. We hope that this article has been helpful.


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