How to Find Equivalent Resistance

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  • 0:00 What Is Equivalent Resistance?
  • 0:47 Calculating Equivalent…
  • 1:32 Example Equations
  • 2:39 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After completing this lesson, you will be able to explain equivalent resistance and use equations to find the equivalent resistance of a basic series or parallel circuit.

What Is Equivalent Resistance?

Before we address what equivalent resistance is, we should first define resistance itself. Resistance is a measure of how much a component or material resists the flow of electricity through it, measured in ohms. It's inversely proportional to current: more resistance means less current will flow; less resistance means more current will flow.

Equivalent resistance may sound like a complex term, but it's really not. It's just a fancy way of saying total resistance. When you have a circuit with more than one component in it, we need to have a way of calculating the total effective resistance of the whole circuit or of one part of the circuit.

Calculating Equivalent Resistance

The way we calculate equivalent resistance depends on whether we're working with a series or a parallel circuit. A series circuit is one where all the components are connected in a single, continuous loop. A parallel circuit is one where the components are connected in separate branches. The method we use to calculate equivalent resistance is different for each type of circuit.

Series vs. Parallel Circuits

For a series circuit, we simply add up the resistances of each component. However, in a parallel circuit, the reciprocal of the total resistance is equal to the sums of the reciprocals of the resistances of each branch.

Equivalent Resistance for Series vs. Parallel

Let's go through an example of each type.

Example Equations

Let's say you have a series circuit containing a resistor, a bulb, and a battery. The resistor has a resistance of 6 ohms, and the bulb has a resistance of 3 ohms. What is the equivalent resistance of the circuit?

Simple: 6 + 3 = 9 ohms

Series Example
Series Example

But now if we connect those two components in a parallel circuit, our calculations get a little more complex. We can say that the reciprocal of the total resistance equals one over six, plus one over three.

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