# Series Resistances

## Introduction

When resistors are connected in series, the combination has an equivalent resistance that is the sum of the resistances of the individual resistors. Mathematically, for a set of N series resistors, this can be stated as:

${R_{eq}} = {R_1} + {R_2} + \cdots + {R_N}$

Where R1, R2, ..., RN are the resistances of the N individual resistors.

This property can be useful in creating desired resistance values from a limited selection of fixed resistors. In this project, we will create a 9 kΩ resistor from the resistors available in Digilent's analog parts kit.

##### After you're done, you should:
• Understand how resistors behave in series.
• Know how to build a circuit with a desired total resistance using a limited selection of fixed resistors.

## Inventory:

Qty Description Typical Image Schematic Symbol Breadboard Image
1 6.8kΩ Resistor
1 2.2kΩ Resistor
1 Digital Multimeter (DMM)

## Step 1: Construct the Circuit

1. Connect the resistors in series and use V+ to apply 5V voltage across the resistors, as shown.

2. You will use your DMM to measure the current I into the series combination of resistors.

## Step 2: Verify Overall Equivalent Resistance

1. Apply power to the circuit. (Open the WaveForm's™ voltage instrument, turn on V+.)

2. Measure the current I.

3. Using the current I, the 5V across the series combination of resistors, and Ohm's law, calculate the equivalent resistance of the series resistors, Req.

4. Using the equivalent resistance formula from the introduction and the measured resistances of the individual resistors, calculate the expected resistance of the series combination of resistors.

5. Calculate the percent error between the expected value and the measured value of the equivalent resistance. Use the formula below to do this.

${\rm{Percent Difference = }}\frac{{{\rm{Measured Value - Expected Value}}}}{{{\rm{Expected Value}}}}x100$

1. Use your DMM to measure the resistance of the combination of series resistors. (Be sure to disconnect the voltage source from the resistors before you do this—you DO NOT want to include the resistance of the voltage source in your measurement.)

Calculate a percent error between the resistance measured with your DMM and the expected resistance you determined in Part 4 of Step 2. Use the formula provided in Step 2.

2. Interchange the locations of the 6.8 kΩ and 2.2 kΩ resistors and re-measure the equivalent resistance. Verify that the location of the individual resistors in the series combination doesn't affect the equivalent resistance.

3. Add resistors to the circuit in this project to create a 12 kΩ resistor. Measure the resistance of the circuit you created and compare your expected value with the measured value. How close can you get to the design requirement?

#### Challenge Problem

• If you are confident in your knowledge of resistors and would like some extra practice, we have provided an extra problem in the link below. This problem requires that you understand the concepts introduced throughout this exercise.