# Series and Parallel Resistors

### Overview

Two or more resistors can be combined in series or parallel. The combined pair of resistors has a total resistance that is different from the individual resistor values. This is a consequence of Kirchoff's voltage and current rules and the definition of resistance. Combining resistors can be very useful when trying to make a resistor of a certain value from standard (E24) value resistors. It is also useful to combine resistors to a achieve a higher overall power rating. For resistors in series, the total resistance is always greater than the largest of the individual resistors. For resistors in parallel, the total resistance is always less than the smallest individual resistor value.

### Learning Objectives

• Appreciate what happens to the total resistance of a pair of resistors in series
• Use the series resistor equation to calculate the equivalent total resistance of two resistors in series
• Appreciate what happens to the total resistance of a pair of resistors in parallel
• Use the parallel resistor equation (in both forms) to calculate the total resistance of two resistors in parallel
• Use the series and parallel resistor equations to make non-standard resistor values from the standard E24 series values
• Be able to extend the series and parallel resistor rules to include three or more resistors in either series or parallel
• Be able to extend the series and parallel resistor rules to include networks containing three or more resistors in some combination of series and parallel

### Lesson Content

Reading: Read the introduction and the first two sections about series resistors and parallel resistors. Make a note of the general principles and the different equations that can be used.

Video (6 min): Watch the video that demonstrates how two resistors combine in series or parallel using actual resistors and a resistance meter.

Video (4 min): Watch an interactive white board video looking in more detail at parallel resistors and networks containing more than two resistors. Add to your notes about series and parallel resistor calculations.

Reading: Read the next section of the web page about combining resistors and why this might be necessary. Add to your notes to include details of making non-standard resistors and increasing power handling.

Video (8 min): The interactive white board vide shows how to derive the equations for series and parallel resistors from Kirchoff's laws. Learn the derivations to develop a better understanding of the underlying theory.

Exercises: Complete the problems to check your understanding.

### Lesson Review

Review your learning by working through the presentations or notes which summarise the website content.

Presentation: Powerpoint download. A powerpoint presentation that considers numerous examples of combining resistors in series and parallel. The examples are different from those on the website.

Notes: PDF download. The website presented in note form as a PDF document.

### Self Assessment

Complete either the questions (pdf download) OR the on-line quiz. They are the same questions.

Quiz: Online quiz about calculating series and parallel resistor combinations.

### Self Evaluation

I can:

• Calculate the combined resistance of two resistors in series
• Calculate the combined resistance of two resistors in parallel
• Use the series and parallel combination rules to make non-standard resistor values from the resistor values available in the E24 series of resistor values
• Calculate the combined resistance of three or more resistors in series
• Calculate the combined resistance of three or more resistors in parallel
• Understand the derivation of the equation for combining resistors in series
• Understand the derivation of the equation for combining resistors in parallel
• Use the series and parallel resistor rules in turn to calculate the overall resistance of a network of resistors in some combination of series and parallel