AP Physics Resistance and Resistivity Lab
Purpose
The goal of this lab exercise is to measure electric current through a metal sample and determine the relations between voltage, current, resistance, and the physical properties of the metal.
Overview
The basic procedure of this experiment is to send a known current through a metal conductor and measure the electric potential difference (or voltage) across a certain length. This entails connecting a conductor to a power source. This is an “unusual” thing to do! A large current can and will occur, depending on the voltage of the power source. For example, if you connect a wire to an ordinary battery the wire will heat up and quickly discharge the battery.
Procedure
A thin strip of “standard” aluminum foil will be used as the metal sample. In order to maximize the resistance it is desirable to have a very narrow and very long strip. Use a marker and a ruler to mark the foil and then cut it carefully into a rectangular strip. Reasonable dimensions for this experiment are a strip with width 2 mm and length 305 mm. (The “length” of this suggested strip is the standard “width” of an ordinary roll of foil.) As is often the case in a scientific experiment, a larger sample size has some advantages, so a longer strip may be marked and cut if so desired (though it is challenging to cut it out).
The strip will be quite fragile and can be broken easily.
Use tape to secure the strip flat on a hard nonconducting surface like a table
top. Leave part of each piece of tape sticking up from the table and fold the
end of the foil as shown. This creates connectors for forming a circuit –
alligator clips attached on each tab will make electrical contact without
ripping the foil.
The Vernier circuit board will serve as the power supply for this experiment. The switch SW1 is convenient to use as an “on/off” switch for the 3 V battery (external = off if nothing is connected to terminals J1 and J2). The internal 3 V battery will be in series with one or more resistors or resistor combinations (details – keep reading!). Basic schematic for both parts A and B:
Turn the circuit off or disconnect whenever you are not actually making a measurement! Because there will be small resistance, the batteries will lose energy rapidly. Resistors on the board will be used to add resistance to that of the foil strip so as to limit the drain on the batteries. There must always be at least one resistor in the loop (minimum of 10 ohms).
Construct the single loop circuit in which current passes in turn through the battery, the resistor(s), the ammeter, and the foil strip. Make an initial connection from terminal 1 to terminal 2 to connect the 3V battery to the 10 ohm resistor R1. Use jumper cables to connect a multimeter, functioning as an ammeter – connect terminal 3 of to the terminal labeled mA on the meter, connect the COM terminal of the meter to one end of the foil strip. Connect the other end of the foil strip to terminal 35. This forms a single continuous loop through which a certain current can flow when the switch SW1 is moved to “3 V”.
The voltmeter will be connected across the entire foil strip for Part A and only across smaller and smaller pieces of the strip for Part B. Keep reading!
Tips for using the multimeter as an ammeter:
Check the meter for proper connections to the mA and COM terminals and then switch the selector to the mA setting. In this condition, the multimeter has very low resistance and indicates the conventional positive current entering through the mA terminal and exiting the COM terminal. The reading will be negative if the current is opposite. The maximum measurable current is 300 milliamperes (anything beyond this may blow the internal fuse).
Tips for using the multimeter as a voltmeter:
Check the meter for proper connections to the V and COM terminals and then switch the selector to the V setting. In this condition, the multimeter has very high resistance and indicates the potential difference of the V terminal relative to the COM terminal. The reading will be negative if the potential is higher at the COM terminal than at the V terminal. In this experiment the values will typically be measured in millivolts, which shows as mV in the display.
Part A – Voltage vs. Current (constant length)
Connect the voltmeter to each end of the foil strip. The value of R in the schematic will be changed to adjust the current through the strip. The current through the foil strip and the voltage across it should be recorded for each trial. Measure and record the length and width of the foil strip. Note – the length recorded should always be the distance between the points at which the voltmeter is connected. The resistor R can be a can be a single resistor or any convenient combination (series and/or parallel) of resistors available on the circuit board. It is best to have trials with values of R spread out across a range from 10 to 70 Ω. (An example of convenient values: 10 Ω, 20 Ω, 25.5 Ω, 51 Ω, 68 Ω) Note: the “infinite” value can be achieved by having an “open circuit” or “air gap”.
Part B – Voltage vs. Length (constant current)
Disconnect the voltmeter from the ends of the foil strip, but leave the rest of the circuit intact. Remove any alligator clips from the ends of the voltmeter’s probes. Return the value of R to 10.0 Ω and do not change it – in order to keep the current constant. Turn on the battery and then simply press the two voltage probes straight down on the foil strip a convenient distance apart. Record this distance as the length – it is not necessary to cut the strip to different lengths! Use the switch to turn the battery on and off – current is needed only when measuring the voltage!
Analyses
Create appropriate, well-labeled, high quality graphs based on the data tables for Part A and Part B. Include an appropriate curve-fit and corresponding equation for each.
Questions
1. What type of relation exists between voltage and current? How does your data support this? Is the aluminum foil ohmic? Be specific and refer to the graph(s).
2. (a) Using the accepted value for the resistivity of aluminum, determine the expected resistance of the foil strip in Part A based on its length, width, and thickness. If you cannot find a better value for thickness just assume a typical value for regular household aluminum foil: 0.016 mm. (b) State the resistance based on measurements of current and voltage, as shown by the appropriate coefficient from the line of best fit for Part A. (c) Determine the percent difference in the two values for resistance. Show all work.
3. (a) Use the width, thickness, and value of the slope from Part B to calculate the resistivity of the metal strip. (b) Determine the percent error in this experimental value.
4. Discuss error.
Part A
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Foil length: |
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Foil width: |
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External R (Ω) |
I (mA) |
ΔV (mV) |
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Part B
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Foil width: |
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Current: |
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Length (cm) |
ΔV (mV) |
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