NETWORKS: RESISTANCE LAB



CEE102

NETWORK LAB

October 8, 2001

Joseph Henry’s Telegraph and The Resistance of Wires

THEORETICAL

Before beginning the individual sections of the lab solve the following short problems to familiarize yourself with the equations and concepts used in the lab.

OHM’S LAW: V = I R (voltage = current x resistance)

Series Resistor: Rtotal = R1 + R2

RESISTANCE LAW: R = (L / A (( = resistivity constant ; L = length ; A = area)

1. In the following circuit what is the current in the loop?

2. In the following circuit what is the voltage across the copper wire?

3. Joseph Henry used a copper wire that was 1/40th inch in diameter and 1/5th mile in length. The resistivity constant for copper is 0.67 x 10-6 ohm-inches. One mile is 5282 feet. What was the resistance of the wire?

CEE102

Joseph Henry's Telegraph and Ohm's Law

The purpose of this laboratory is to understand the consequences of resistance of wires in the design of electrical information and power networks. The laboratory begins with an examination of Joseph Henry's Telegraph of 1829 as shown below.

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Henry's telegraph consists of a horseshoe electromagnet, a 10-inch-long bar magnet, and a bell. When the electromagnet is energized the bar magnet rotates either towards or away from the bell, depending upon the direction of current in the electromagnet coil. A sulfuric-acid zinc-copper battery is used as the voltage source.

Joseph Henry operated this telegraph for his students at the Albany Academy three years before he came to Princeton and three years before Samuel Morse came up with the idea of a telegraphic code and system. Joseph Henry taught natural philosophy (physics) at Princeton during the years 1832-48. While at Princeton he built several variations of his telegraph, including one in 1835 that connected his laboratory and his home using a wire strung up in the elm trees in front of Nassau Hall. Joseph Henry's laboratory was in Philosophical Hall, an architectural twin to Stanhope Hall, which was located in the spot that Chancellor Green now occupies. His home, The Joseph Henry House, was then located behind and between Stanhope Hall and West College. In 1846 Henry left Princeton and became Secretary to the Smithsonian Institution, a position that he held until his death in 1878.

In Henry's original lecture demonstrations, a bell was struck by energizing an electromagnet with the battery that drove current through one-fifth-mile length of wire. The long wire was strung around the classroom. To ring the bell, Henry found it necessary to replace the usual low voltage galvanic cell with a high-voltage battery (that is, one consisting of many cells), and he also had to greatly increase the number of turns of wire wrapped about the horseshoe magnet core. These two modifications allowed the telegraph sounder to operate when it was a great distance from the power source.

In the modern context Joseph Henry's modifications seem obvious, however, at the time these modifications were entirely original and very significant. Consider the fact that insulated wire did not exist at the time Henry was carrying out his experiments. In order to wrap many turns of wire about the horseshoe magnet core, Henry had to insulate the wire. He used a wrapping of silk thread. In later coils he used cloth as an insulator. Joseph Henry was the first to realize the importance of using many turns of wire as a method to increase the strength of electromagnets. In later experiments he used many turns to produce magnets capable of lifting weights of several thousand pounds. Whenever you see a magnet with many turns or a large electric motor with many turns you should think of Joseph Henry.

Henry's telegraph sounder operates because the direction of current determines the polarity of the magnetic poles in the horseshoe electromagnet. The magnitude of current in the electromagnet coil and the number of turns set the strength of the poles. The magnetic field strength, B, between the poles is,

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where I is the current, N is the number of turns, and k is a constant that depends upon the magnetic properties of the magnet core. The armature magnet pole that is between the poles of the horseshoe electromagnet moves in a direction governed by the repulsion of like poles and the attraction of unlike poles. Therefore, in one direction of current in the electromagnet circuit, the magnet armature rotates away from the bell. In the other direction it rotates towards the bell, striking it and making a sound. A plan view of this configuration is illustrated below.

The current in the circuit is reversed by interchanging the connections to the battery. The bell is made of a non-magnetic material such as brass to prevent the armature magnet from sticking upon first ringing. Observe that the bell sounder device has similarities to a motor in that a current produces torque and motion. Shortly after building this first telegraph sounder, Henry built the first practical electromagnetic machine - a rocking beam electric motor.

Henry had to figure out a way that the sounder would operate when it was placed at a great distance from the battery. In his demonstration of this device to students at the Albany Academy, the battery and sounder were separated by a very long distance of wire. The high resistance of the long transmission wires diminished the current flowing in the circuit preventing the sounder from operating strongly. Henry's solution was to use a high-voltage battery to boost the current in the circuit and to wind a great number of turns of wire on the horseshoe magnet core to increase the strength of the magnetic force. (Samuel Morse in later work used these same ideas.)

To understand why it was necessary to use a high-voltage battery one needs to appreciate the formulas for the resistance of wires and Ohm's law. Ohm's law relates voltage (electrical pressure) and current (electrical flow) though the concept of resistance. The law states that,

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and defines the concept of a resistance. The law for the resistance of wires is,

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where R is resistance, ( is the resistance constant - a property of conducting materials, L is wire length, and A is wire cross-sectional area. Henry used copper in his experiments because it has a very low value of the resistance constant.

We see from the second formula that the total resistance of the wire increases linearly with wire length and inversely with wire cross-sectional area. Henry used wire that was 1/40th to 1/20th inch in diameter. In one of the warm-up problems you will calculate the resistance of the wire in Henry's original circuit.

The first formula is Ohm's law that expresses a linear relationship between the voltage and the current. The higher the voltage the higher the current in the circuit.

We now understand why a high-voltage battery was needed. The increased resistance of the long wire (resistance R = (L/A) decreased the current in the circuit (I=V/R). The decreased current reduced the magnetic field (B=kIN) and therefore reduced the torque on the magnet armature. By using a higher voltage battery Henry was able to overcome the reduced current that was the result of the increased resistance of the very long wire that was added between the battery and the sounder.

In the laboratory, you will measure the resistance of wires of varying lengths and diameters and understand the relationship between length and cross-sectional area. Ohm's law for these wires will be tested using the circuit shown below.

The resistor voltage is measured using a voltmeter connected across the resistor. The current is calculated* from Ohm's law (I = V/R). Since the resistor is in series with the wire, the current flowing through the resistor is equal to the current flowing through the wire. The voltage drop across the wire is also measured with a voltmeter and its value is plotted along with the computed current in the circuit. The measurement is repeated and plotted for numerous voltages of the power source. The resulting curve is the current-voltage relationship of the wire. The curve is linear if the object under test follows Ohm's law. Wires are linear and follow Ohm's law precisely with a constant R.

In another measurement you will use the circuit above to observe the current-voltage relationship for an incandescent lamp. A lamp filament is typically a heated wire, therefore you might expect its current-voltage relationship to mimic that of the long copper wires that you have just measured. However, you will observe that the lamp curve differs significantly from that of the long copper wires in that it is not linear.

The non-linearity is a consequence of the fact that the resistance constant depends on temperature, and the temperature of the lamp filament increases significantly as the current flowing through it increases. When the temperature of the wire approaches the temperature of a candle flame (i.e., several thousand degrees centigrade) it emits light. The light is the result of vigorous motion of electrons in the wire. The change of resistance with current is in contrast to the measurements that you made on copper wires where the temperature did not vary appreciably for the currents used.

The currents used in the earlier measurements on copper wires were sufficiently low that the temperature rise with current was insignificant. If you measured the current-voltage relationship for copper wires under circumstances of high enough current that the wires would glow red hot, a non-linear curve similar to that of the lamp would be obtained.

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• It may be noticed that in some sense we use Ohm's law to check Ohm's law. While not ideal, we do this because the PASCO measuring system used in the laboratory works with voltages only, not currents. As a result we only indirectly "measure" the current in the circuit. Experiments performed in the 19th century checked Ohm's law using ammeters, not voltmeters. 19th century ammeters caused a rotation of a magnetic needle by a magnetic field produced by current flowing in a coil of wire. The deflection of the magnet needle was therefore a more direct measure of the current, since the magnetic field in a coil is directly proportional to current. The 19th century experimenter, however, did not have a good voltmeter. Here the experimenter used an ammeter in series with a large resistor to infer the voltage drop between two points using Ohm's law, that is, V = IR, where R is the resistance of the large resistor.

NETWORKS: The Resistance of Wires

EQUATIONS

The equation governing the relationship between current, voltage and power is:

P = V I

Because V = I R the above equation can also be expressed as:

P = I2 R

In the equations above the variables have the following meanings:

P is the power lost to heat and is measured in Watts, W

I is the current and is measured in Amperes, A

R is the resistance and is measured in Ohms, (

V is the voltage and is measured in Volts, V

Resistance of a wire is determined by the equation

R = ( L /A

( is the resistivity constant of the material and is given to be 0.67 x 10-6 ohm-inches for copper

L is the length of the wire and A is the cross-sectional area of the wire.

Series Resistance

Rtot = R1 + R2

SETUP

This lab uses Microsoft Excel in conjunction with a computer interface board and our own lab equipment. Excel allows us to use the computer to generate incremental signals over time. At each time interval the computer outputs a specific voltage, which is specified in an Excel spreadsheet.

This is a picture of the lab setup:

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• On the left is a large metal box. This is the power supply and has an on/off switch on the back.

• On the upper left is a rectangular green board. This is the computer interface. On the top of the board is a computer port where we connect the computer cable to the board.

• On the bottom right is a circuit with various meters. This is our test board. On this board we have the components of a simple circuit.

A closer look at the circuit:

• At the bottom of the board we have two wires coming in from the power supply (metal box) this acts as a variable power source which operates at a level between 0 to +5 V.

• In the middle of the board we have a known resistor of 3( and two wires connected to the meter and to the computer interface. These two wires allow the computer to measure the voltage across the resistor and thus let us calculate the current (I) in the circuit. We can calculate the current using I = V/R.

• On the right side of the board is where we determine the voltage across an unknown resistor such as a length of wire or a light bulb. Similar to the connections mentioned above, two wires connect to the computer interface and allow the computer to measure the voltage across the unknown resistor.

The computer interface also is attached to the power supply to regulate the voltage in the circuit. Thus at each time interval the computer will provide a known voltage and then it records the voltage across the known and unknown resistors on the test board.

The Unknown Resistors:

In this lab we will be using a number of different wires and bulbs in an effort to determine their resistance at different applied currents. The three different wires will be 150-foot lengths of insulated copper wire each with different diameters:

AWG 26 diameter = 0.0159 inches

AWG 28 diameter = 0.0126 inches

AWG 30 diameter = 0.0100 inches

We also will be using two different light bulbs with different resistance. Bulb 1 has a bayonet type base and has a nominal rating at 6 volts and 0.5 amps. Bulb 2 has a screw base and operates nominally at 14 volts and 0.214 amps.

Before we use the computer we will use meters on the test board to verify our lab setup.

Thus before we run the Excel lab we will provide the system with a 1.5V, 3V, and 4.5V power supply (via batteries) and check to see if our readings concur with our calculations.

PROCEDURE

Part 1 – Manual Measurement of Current versus Voltage for a Wire -- Hand Calculations

First try to make the replica of Joseph Henry’s telegraph work. You should hook up a battery pack (1.5V, 3.0V, or 4.5V) to the horseshoe magnet. Using the polarity reversing knife-edge switch, you should be able to ring the bell. A long length of wire between the battery and the telegraph will make it more difficult to operate. This laboratory is focused on understanding why.

Next make sure that the power supply from the metal box on the left has been switched to OFF and that it is disconnected from the test board.

1. Observe that one of the voltmeters on the board measures the voltage of the power supply. Another voltmeter is connected across the known 3( resistor. This voltmeter will allow us to compute the current in the circuit by applying Ohm’s Law, I = V/R. There is also a current meter (ammeter) in the circuit which will allow us to measure the current directly to check the computation.

2. Insert an “unknown” resistor in the right side, try using one of the lengths of wire marked “150 feet @ 26 gauge”

3. Observe that the third voltmeter on the board is connected across the “unknown” resistor.

4. Plug in the two leads from the battery pack labeled 1.5Volts to the bottom section of the test board. (Make certain that the metal box is disconnected from the test circuit.)

5. Now with the battery completing the circuit, record the readings from the three voltmeters and the one ammeter.

6. Detach the battery and repeat steps 4 and 5 with a 3 volt battery pack and a 4.5 volt battery pack.

7. Use the information collected to compute the current in the circuit. Check that the computed current is equal to the measured current. Check also that the measured power supply voltage equals the sum of the voltage across the unknown resistor and the known resistor. (Why?) Finally plot a curve of the current versus voltage for the unknown wire (using Excel) and determine the resistance of the wire.

8. Verify the observed resistance of the wire with the theoretical resistance that can be calculated by using the equation: R = ( L /A.

Part 2 – Automated Measurement of Current-Voltage Relationship for Wires and Bulbs

Now that we have a hands-on understanding of the test apparatus and how the circuit works in helping us determine the resistance of the unknown resistors we can use the computer interface in combination with Microsoft Excel to help us automate the tasks. This will provide us with a larger number of small voltage steps and more accurate readings.

Make sure to detach the battery supplies from Part 1.

1. Attach the leads coming from the power supply (metal box) to the bottom of the circuit board.

2. Make sure that there is an unknown resistor (wire/bulb) on the right side of the board.

3. Observe the two sets of leads coming the computer interface board that are in parallel with the voltmeters across the known and unknown resistors on the test board.

4. Now turn on the power supply and open the Excel spreadsheet label “I-V Curve Tracer”.

5. The spreadsheet is set up in the following manner. The left most column specifies the voltage that will be provided to the circuit via the power supply. The column labeled VR designates the readings at each time interval of the voltage across the known resistor (3 Ohms) and the column VX designates the voltage readings across the unknown resistor (wire or bulb). The computer than uses the same procedure that was carried out in Part 1 to determine the current in the circuit and the effective resistance of the unknown resistor.

6. Start the computer automation by pressing Alt+F8 and then hit Enter.

7. Watch as the highlighted cell moves slowly down the column of input voltages and then updates the values of the voltages in column VR and VX. Observe that the meters on the test board move as the automated data collection progresses. If you are using a light bulb as the unknown resistor then you will be able to notice the bulb’s intensity changing as the voltage changes.

When the computer program is finished, create a graph (using Excel) of the current(I) versus the voltage(V) for the unknown device. From this curve it is possible to determine the effective resistance of the unknown resistor

8. Make sure to repeat all the steps in Part 2 for each unknown resistor (5 wires and 2 bulbs) and print out the graphs for all of them. The 5 different wires that need to be tested are:

75ft, 150ft, 225ft @ 26 gauge, 150ft @ 28 gauge, 150ft @ 30 gauge

In addition create graphs of the following relationships:

• R vs. L (resistance versus length of the wire)

• R vs. 1/A (resistance versus the 1 over the area of the wire)

Make sure to print out your Excel graphs to be included in you report.

Comments and considerations:

• How do the results of your hand calculations and voltmeter readings from Part 1 compare to the results in Part 2?

• There obviously is a difference between the shape of the graphs between the light bulbs and the wires. What does this represent?

• How does temperature effect the resistance of the light bulb “wire”? Why didn’t you notice this in Part 1?

• Where on the graphs for the two bulbs is the normal operating point.

• Why was it necessary for Joseph Henry to use a higher Voltage battery and more turns of wire in his electromagnet when the battery and the bell ringer were connected through 1/5th of a mile of wire.

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Voltmeter

3 Ohm Resistor

Voltmeter

Voltmeter

N

Telegraph Sounder

Joseph Henry's Telegraph of 1829

Current-Voltage Curve-Tracing Circuit

WIRE

BATTERY

RESISTOR

electromagnet

armature

pivot

S or N

N or S

bell

S

Ammeter

Unknown Resistor

Power Supply

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