Physics Laboratory 6

Resistance Measurements

In this lab you will determine the resistance of different resistors by

Background:

imageAny device that offers resistance to current flow has an equivalent resistance.  If a voltmeter is used to determine the voltage V across the device and at the same time an ammeter is used to measure the current I flowing through the device, then this resistance can be found by dividing V by I, i.e.  R = V/I.

The resistance of the device can also be determined with an ohmmeter.  A simple ohmmeter is a voltage source V in series with an ammeter.  The component, whose resistance is to be measured, is disconnected from any circuit and the ohmmeter is connected across it.  The equivalent resistance is R = V/I, where I is the current flowing through the ammeter.  The resistance of the component is R minus the (usually very small) resistance of the ohmmeter itself.

The accuracy of an ohmmeter is limited by its internal resistance.  When extremely accurate measurements are needed, a Wheatstone bridge is used.  A diagram of a Wheatstone bridge is shown on the right.  A Wheatstone bridge uses four resistances.  R2 is precisely known, it is the reference or standard resistance.  The ratio R3/R4 can be adjusted, but its value is always known.  The diagram shows a single coil that is divided by the tap B.  The ratio of the resistances R3 and R4 equals the ratio of the corresponding lengths of coil.  This device is called a potentiometer.  Rx is the resistance to be determined.  A power supply with a switch is connected across points C and D, and a digital voltmeter is connected across points A and B.

The Wheatstone bridge uses a null measurement to determine the unknown resistance.  When the voltmeter reads zero, the potential at A equals the potential at B.  The bridge is balanced.  When the bridge is balanced, the voltmeter reading does not change when the switch is opened and closed.  Such null measurements are the basis for the most accurate instruments, because, when no current is flowing through the meter, the internal resistance of the meter does not affect the circuit.

If points A and B are at the same potential, then we have

I1Rx = I3R3,
I2R2 = I4R4.

Since no current is flowing through the voltmeter we have

I1 = I2,
I3 = I4.

Therefore we have

Rx/R2 = R3/R4
Rx = R2(R3/R4).

The unknown resistance is determined by reading the ratio R3/R4 of the potentiometer when V = 0.  The dial of a potentiometer displays a number n.  For the potentiometer used in our experiment, n/10 is equal to the ratio R3/(R3 + R4).  We can solve for R3/R4.

R3/R4 = n/(10 - n).

Therefore, when V = 0, we have for the unknown resistance

Rx = R2n/(10 - n).


When a manual refers to a resistor, it usually refers to a device whose only purpose it is to offer resistance to current flow.  The resistance of a resistor is often printed onto the resistor in code.  A pattern of colored rings is used.  Most resistors have three rings to encode the value of the resistance, and one ring to encode the tolerance (uncertainty) in percent.  The colors of the rings are internationally defined to represent integers between 0 and 9.  The integers represented by the different colors are shown in the table below.

Black

Brown

Red

Orange

Yellow

Green

Blue

Violet

Gray

White

0

1

2

3

4

5

6

7

8

9

image

Resistor Color Codes

Color 1st and 2nd
Significant
Figures
Multiplier Tolerance
Black 0 1 --
Brown 1 10 ±1%
Red 2 100 ±2%
Orange 3 1,000 ±3%
Yellow 4 10,000 ±4%
Green 5 100,000 --
Blue 6 1,000,000 --
Violet 7 10,000,000 --
Gray 8 100,000,000 --
White 9 -- --
Gold -- 0.1 ±5%
Silver -- 0.01 ±10%
No Color -- -- ±20%

Link:  Resistor Color-Code Calculator


Open a Microsoft Word document and keep a log of your activities.  Answer all the questions in blue font.

Exercise

Find the nominal resistance of three color-coded resistors and the nominal uncertainty in this value.  Record this in table 1 below.

Table 1

Resistors
Nominal R
Ω
Tolerance
%
R1 image

 
R2 image

 
R3 image

 
Series


X
Parallel


X

Experiment

You have 5 coils of wire, a standard resistance box containing 1-10 ohm precision resistors, a potentiometer, a voltmeter, and a 10 V power supply.  You will measure the resistance of each of the coils with a Wheatstone bridge.  With a switch you can select which standard resistor from the you want to use in the bridge.

image

Four coils are made of copper wire and one coil is made of nickel silver wire.  The length and the radius of the wire and the resistivity of the material for each coil are listed in the table below.  You will also calculate the resistance of each coil from these given material properties.

Data describing the coils

Coil #
Type
resistivity
(10-8Ωm)
Length L
m
Radius
(10-4m)
1 copper 1.7 10 3.2
2 copper 1.7 10 1.6
3 copper 1.7 20 3.2
4 copper 1.7 20 1.6
5 nickel silver 33 10 3.2

 

A schematic diagram of your Wheatstone bridge circuit is shown below.

image

Table 2

Coil #
n
R2
Ω
Measured Rx
Ω
Calculated Rx
R = (ρL/A)(Ω)
Difference
%
1          
2          
3          
4          
5          

Some hints



Convert your log into a lab report.

Name:
E-mail address:

Laboratory 6 Report

Save your Word document (your name_lab6.docx), go to Canvas, Assignments, Lab 6, and submit your document.