# Finding the Equivalent Resistance: Series, Parallel & Combination Circuits

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• 0:01 Equivalent Resistance
• 1:21 Series Circuits
• 2:40 Parallel Resistance
• 3:47 Combination Circuits
• 5:14 Lesson Summary

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Lesson Transcript
Instructor: Christopher Muscato

Chris has a master's degree in history and teaches at the University of Northern Colorado.

How does resistance impact the way that electrical currents flow through a circuit That's what we are exploring in this lesson. We'll check out resistance in the three main kinds of circuits and practice calculating this value.

## Equivalent Resistance

Resistance is futile. No, resistance is the duty of an oppressed people. Or, maybe resistance is just a matter of physics. Although it may seem a bit less dramatic than a revolution of the people against the tyranny of a despotic king, resistance in electrical circuits is still a pretty important part of modern society. A really important part, actually. When talking about electricity, resistance is the degree to which a material withstands an electrical current. This is measured in ohms, represented by the Greek omega symbol, and the higher the number the greater the resistivity. Copper has low resistivity, so it conducts electricity really well. Rubber has a very high resistivity, and doesn't conduct electricity.

Now, in a circuit board, you'll have multiple circuits directing electricity in multiple ways and made of multiple materials. So, you need to know how well the entire system will conduct electricity. We call the total resistance of circuits the equivalent resistance, and it's pretty important to calculate this correctly. Fail to do so, and, well, your resistance could be simply futile.

## Series Circuits

So, in a complex circuit electricity will be resisted by each individual part differently. Let's start looking at this through a simple arrangement of circuits. This is a resistor, a device that limits or regulates an electrical current. When we have a circuit in which resistors are arranged in a chain, we call this a series circuit. Since the resistors are lined up along a single path, the current only has one path to take and will pass through each resistor. That means that calculating the total resistance is pretty easy.

Basically, you just add them together. The equation looks like this: R=R1+R2+R3â€¦, where R is the total resistance, and an R with a number is each individual resistor. So, in this circuit we have three resistors with resistances of 100 ohms, 150 ohms, and 400 ohms. Plugging that into our equation looks like this: R = 100 ohms + 150 ohms + 400 ohms, which ends up as R = 650 ohms. Now, in a series circuit we usually refer to this as the total resistance rather than equivalent resistance since it's such a simple equation, although really those two terms are interchangeable.

## Parallel Resistance

Okay, so what if your resistors aren't lined up in a neat little row? Sometimes the resistors are arranged so that the heads and tails are facing the same direction but along individual paths. This is called a parallel circuit. Since each resistor has its own branch, the current is broken up, then recombined, so the equation is a bit more complex. It looks like this: 1/R = 1/R1 + 1/R2 + 1/R3â€¦. This means that we're dealing with reciprocals. So, if our three parallel circuits have resistances of 4 ohms, 8 ohms, and 8 ohms, the equation would look like 1/R = 1/4 ohms + 1/8 ohms + 1/8 ohms or 1/R=1/2 ohms. Finish it out and the equivalent resistance ends up as R = 2. In parallel circuits, the equivalent resistance is always lower than the least resistant component.

## Combination Circuits

Now, let's see what this looks like in a really complex circuit. A circuit containing both series and parallel components is called a combination circuit. So, how in the world are we supposed to calculate the equivalent resistance for all of these different parts? It's actually simpler than you might think. Basically, we reduce the total circuit into series and parallel circuits.

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