Series vs Parallel Resistors: How to Calculate Equivalent Resistance

Learn the difference between series and parallel resistors and get simple steps to calculate equivalent resistance for accurate circuit planning.

In the sphere of electronics, whether you’re a hobbyist tinkering in your garage or an engineer designing the next big Internet of Things (IoT) device, it is of fundamental importance to understand what resistors are and what they do. 

Resistors control the flow of electric current in a circuit. However, as multiple resistors are added to a given circuit design, ever-greater complexity is introduced, and it can be difficult to keep track of the full implications of it all. 

This is where the concepts of series and parallel resistors come into play. They enable you to simplify sprawling networks into a single equivalent resistance, thereby making calculations easier and helping to predict how the given circuit will behave under load. 

In this guide, then, we will take you through what distinguishes series and parallel configurations from each other. This will be followed by us setting out how you can determine the equivalent resistance for such circuits. 

What Is ‘Equivalent Resistance’, Anyway? 

Often denoted as Req, equivalent resistance is the single resistance value that would produce the same overall effect on current flow as the entire combination of resistors in your circuit. 

By simplifying to Req, you can treat a complex setup as if it was a simple one. This allows you to save time on voltage drops, power dissipation, and more. 

You might have also come across the term “total resistance”. In most contexts, especially for series or simple parallel circuits, “total resistance” and “equivalent resistance” are used interchangeably, and they generally mean the same thing. 

So, How Can You Figure Out Equivalent Resistance for These Circuits? 

Let’s set out the essentials for both types of configurations: 

• Resistors In Series 

The connection of resistors “in series” means they are linked end-to-end, forming a single path for the current to flow. The total resistance in the circuit goes up as more components are added, because the current must pass through each resistor in sequence. 

The equivalent resistance for a series circuit is the simple sum of all the individual resistances. So, the formula for calculating the equivalent resistance in a series circuit can be expressed as: Req = R1 + R2 + R3 + … + Rn, where R1, R2, …, Rn are the values of the individual resistors. 

• Resistors In Parallel 

Resistors being connected in parallel means they are connected across the same two points. As a result, multiple separate branches or paths are created for the current to flow. 

Contrasting with the situation for series configurations, the addition of resistors in parallel actually causes the total resistance of the circuit to go down. This is because the introduction of a greater number of pathways for the current effectively increases the total current flow. 

When it comes to determining the total resistance of a parallel circuit, then, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances. 

The general formula for calculating the equivalent resistance in a parallel circuit can be expressed as: 1/Req = 1/R1 + 1/R2 + 1/R3 + … + 1/Rn. If there are only two resistors in parallel in the given circuit, this simplified formula can be used: Req = (R1 x R2) / (R1 + R2). 

A Reputable Online Tool Can Help You Perform These Calculations Even Faster 

For professional engineers, students, and hobbyists alike, there is no question that manual calculations using the aforementioned formulas can take a lot of time. Human error may also easily creep in, particularly when dealing with complex series-parallel configurations. 

This is where it can make sense to have a suitable online calculator saved in your browser’s bookmarks. If you navigate to the website of electrical component supplier RS, for instance, you can easily and quickly simplify circuits with the series and parallel resistance calculator there. 

Such user-friendly tools enable you to select the connection type (series or parallel), before inputting your resistor values, and hitting the “Calculate” button. That’s it; you will be immediately presented with the equivalent resistance reading, thereby allowing you to proceed with the rest of your project. We wish you all the best with it! 

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