Linearity of a resistor
Scott D. Johnson
George Leftfield
sdjohnson@pgcc.edu
gleft@baseball.edu
1:00pm-3:00pm 10/21/1980
Laboratory Location: 17th East Street Laboratories, Room 210E

Abstract

This experiment seeks to determine if a 5 ohm resistor is linear to within 5% in the voltage range 0.160 to 2.50 volts. A simple serial circuit was devised and tests showed that the resistor was linear to well within 5%.

Introduction

Common resistors, like ACME off-the-shelf resistors, are usually carbon-composite resistors. An ideal resistor has the mathematical relationship V = IR, called Ohm's Law, where V is the instantaneous voltage across the resistor, I is the current, and R is a proportionality constant that is called resistance. Ohm's law holds in most circumstances however is not valid at extreme temperature ranges, voltage ranges, and high frequencies.

A non-ideal resistor will have a linear range which follows Ohm's Law closely and a non-linear range associated with it. For most applications it is desirable to operate the resistor in the linear range. Testing the linearity of circuits whether they are resistors or other circuit items is commonplace in industry.

Several tests performed by a number of groups seem to indicate that resistors are linear with respect to voltage. However resistors are known to go non-linear in certain voltage ranges. Our group has an application that requires a 5 ohm resistor to be linear between the voltage ranges of 0.160 to 2.50 volts. We believe that an off the shelf resistor found an ACME should be linear to better than 5%. To test this we will measure the current through a resistor with a known applied voltage within the above voltage range.

Materials

Hewlett Packard 6253A DC Power Supply
Fluke T5-600 ammeter
Fluke 189 Multimeter
Connector Board
ACME resistor [1 Watt 5 ohm 10% tolerance (silver band)]

Procedure

1. Using the connector board connect the resistor to the power supply (see diagram).

2. Connect the ammeter in series.

3. Change the voltage to the following 5 voltages: 0.160, 0.300,0.630,1.30, and 2.50 volts (in a cyclic order)

4. Repeat this sequences 5 times recording the current each time.

Results

The results are tabulated in the table (table 1) in the appendix with current readings repeated a number of times to give us a reasonable error bar. The laboratory's temperature was 25 degrees C and had a steady relative humidity of 45% during the experiment.

A linear fit (see figure 1) gives us the following relationship between current and voltage:

I = (0.201 +/- 0.002)V + (0.00112 +/- 0.001)

Figure 1: Fit of current versus voltage. A linear fit is clearly evident with no deviation.

Discussion

The relationship derived in the results is fairly close to the theoretical relationship of I = V/R with R in the range of 5 ohms. We anticipated an intercept of zero in this experiment, however, the linear fit suggests otherwise. This could be an unknown effect of the resistor or power supply however we believe that we did not take enough data to provide a good linear fit. It is our opinion that increasing the number of data points will produce a zero intercept. Further experiments should have more voltage points and more current readings.

While this experiment showed that the resistance is linear within this voltage range, it was very limited in scope. A better experiment would have tested multiple resistors at many voltage levels.

Conclusion

Within the voltage range of 0.160 to 2.50 volts we have determined that resistance is linear. The fit closely matches the theoretical equation I = V/R.

Reference

Electronic Components and Measurements, Bruce D. Wedlock and James K. Roberge, Prentice-Hall, Inc. Englewood Cliffs, NJ (1969).

I've gone far into the future and found a replacement for the above book that is now out of print:

Practical Electronics for Inventors, 2nd edition, Paul Scherz, McGraw-Hill (2007).

http://en.wikipedia.org/wiki/Resistor

Appendix

Table 1: Current versus voltage to determine if the resistor provide is linear within a range of 0.160 to 2.50 volts.

Voltage (V)

Imeasured (A)

<I>

σI

0.160

0.0310

0.0322

0.00130

0.160

0.0330

0.160

0.0310

0.160

0.0340

0.160

0.0320

0.300

0.0610

0.0618

0.000837

0.300

0.0620

0.300

0.0630

0.300

0.0610

0.300

0.0620

0.630

0.140

0.126

0.0134

0.630

0.120

0.630

0.110

0.630

0.120

0.630

0.140

1.30

0.250

0.258

0.00837

1.30

0.270

1.30

0.260

1.30

0.260

1.30

0.250

2.50

0.500

0.502

0.00837

2.50

0.490

2.50

0.510

2.50

0.510

2.50

0.500