# Ohm's Law:

## Introduction

Fixed resistors are fabricated with a nominal resistance value; however, individual resistors will generally not have exactly this resistance—their actual resistance will vary from the nominal value to some extent. In this exercise, we will be measuring the resistance of several resistors that all have the same nominal resistance in order to determine the actual resistor-to-resistor resistance variations. These variations will be compared with the manufacturer's specified tolerances.

We will use some basic statistical analyses in this section to examine variations in resistor resistances. Statistics are a way to quantify variations in results which are due to random effects, such as variations in manufacturing, uncertainty in measured quantities, and measurement noise. Some basic information relative to common statistical quantities used to characterize data is provided in the Basic Statistics link of this experiment.

Microsoft® Excel™ and MATLAB® are software packages which are commonly used by engineers to perform calculations. Both software packages have built-in capabilities for performing statistics. Some Microsoft Excel and MATLAB commands, which can be used to perform the analyses necessary in this exercise, are also provided at the links to the right.

This exercise uses concepts introduced in our experiment on Ohm's law. A link to this experiment is provided in the related materials section as well.

## Step 1

Pick five resistors with the same color code from your parts kit; the third band on the color code should be red. From the color code on the resistors, determine the expected (nominal) resistance of the resistors and record this value.

## Step 2

1. Use your DMM as an ohmmeter to measure the resistances of all five resistors. Record these values.

2. Calculate the mean, median, and standard deviation of the resistance values.

3. Convert these values to percentages of the nominal resistance (using the formula below), and record these results.

4. Determine the manufacturer's tolerance on the resistance values of the resistance and comment on whether your resistors lie within the specified tolerance.

${\rm{Percent}} = {\rm{}}\frac{{{\rm{measurement}}}}{{{\rm{nominal}}}} \times 100$

## Step 3

1. Use your Analog Discovery and DMM to apply 5V to your resistors and measure the resulting current. Record the current and the applied voltage for each resistor.

2. Use the resistor voltage and current to calculate resistances for each resistor; record these values.

3. Calculate the mean, median, and standard deviation of these resistance values.

4. Convert these values to percentages of the nominal resistance (using the formula in Step 2), and record these results.

5. Comment on these resistances relative to the nominal values, the manufacturer's tolerances, and the data measured using the ohmmeter in Step 2.