To investigate the change in the resistance of a coil of wire as the temperature of the coil is varied.
To see that resistance really does change with temperature, and gain some understanding for the size of that change for a typical conductor.
Cutnell and Johnson 20.3. Note Equation 20.5.
When a potential difference, V, exists across a length of metallic conductor it is observed that negative charges flow in the conductor, from low to high electric potential, due to the electric field associated with the potential difference. A charge flow, called a current, I, is taken to be positive in the direction positive charges move in response to an electric field. In real life, many electrical circuits employ currents caused by the motions of electrons, which have negative charge; therefore, the actual direction of motion of the charged particles runs opposite to the direction of the current. A linear relationship is observed between the current through and the potential difference across a conductor. This relationship, called Ohm's Law, is often stated as
V = I * R
but may also be written as
V
R = --- (1)
I
where R
is the
resistance in ohms:
1 volt
1 ohm = ---------
1 ampere
For a conductor of uniform cross-section (such as a wire or rod),
one can calculate the resistance from its material properties:
rho * L
R = --------- (2)
area
where
rho = resistivity of material (Ohm-meters)
L = length of conductor (meters)
area = cross-section area (meters*meters)
For most materials, the resistivity changes with temperature.
If the temperature range is not too large, the resistivity is a linear
function of the temperature, T, and can be expressed as
rho(T) = rho(T0) * [ 1 + a(T - T0) ] (3)
where
T0 = reference temperature (deg Celsius)
T = temperature of interest (deg Celsius)
rho(T0) = resistivity at reference temperature (ohm-meters)
rho(T) = resistivity at temperature of interest (ohm-meters)
a = temperature coefficient of resistivity (1/deg Celsius)
When a
tabulated for several different materials,
as it is in your textbook, the reference temperature is
usually 20 °C.
We will use the same value in this experiment.
As the temperature of a conductor is varied, its resistance changes due to
For copper, which you will be using in this experiment, the thermal expansion effects are more than 200 times smaller than the effect of the resistivity change. We may ignore the thermal expansion effects completely in this experiment, considering the precision of our measuring devices. Since only the change in resistivity of the material is important, the overall resistance of the conductor has a similar dependence on temperature:
R(T) = R(T0) * [ 1 + a(T - T0) ]
= R(T0) + R(T0)*a*(T - T0) (4)
where
T0 = reference temperature (deg Celsius)
T = temperature of interest (deg Celsius)
R(T0) = resistance at reference temperature (ohm)
R(T) = resistance at temperature of interest (ohm)
a = temperature coefficient of resistivity (1/deg Celsius)
The temperature coefficient a is the same as
that given above for the resistivity.
If the resistance of a conductor is measured at several different temperatures, a graph of the data will be linear with a slope of a * R(T0) and a vertical intercept at T0 of R(T0).
Safety Precautions: Don't touch portions of the apparatus which are hot!
In this experiment, you will determine the resistance of a coil of copper wire while its temperature is varied from room temperature to near boiling temperature. The resistance will be calculated from a measurement of the potential difference across the coil and a measurement of the current passing through the coil. The potential difference and the temperature will be measured automatically by the computer through sensors connected to the interface. The current will be supplied by a constant-current source (a DC power supply) and is measured using a digital multimeter.
The stockroom staff should have set up the power supply for you, so you should not have to make any adjustments. However, if it has been mis-adjusted, you may need to adjust the controls as follows:The constant-current indicator (red light) should be lit up on the power supply's front panel. If the green light is lit, your circuit is receiving constant voltage, not a constant current; ask your lab instructor to fix the situation.
- turn all knobs fully counterclockwise (to zero)
- turn the upper voltage knob about 1/2 of a turn clockwise (so the little white line on the knob moves to about 12 o'clock)
- slowly turn the "fine adjust" current knob (far left) clockwise, while you watch the multimeter's display
- stop when the multimeter display reads about 80. The display's units are milliamps at this setting, so the current will be about 80 milliamps.
The sensors should have been set up by the stockroom staff. Just in case they need to be adjusted:
You may see an error message which says "Sensor Conflict". Correct the Ch1 sensor by using the pull down menu to the right to choose "Raw Voltage, 0-5V", then click "OK." The error message should disappear.
- From the menu, choose Setup, then Sensors.
- Click on Ch1 and set sensor to "Raw Voltage", in the range 0-5 Volts.
- Click on Ch2 and choose "Stainless Steel Temperature." from the sensor menu.
You must calculate values of
The Logger Pro program should have been set up for this experiment when you start. You will need only to make two small adjustments to its default values.
At this point, you should see a Red Collect button at the top of the screen, alongside the menu controls File,Edit, etc. If you do not see a Collect button, then Save the current session into a file on disk, then quit and re-start Logger Pro. This is a known bug :-(
You should make graphs of the resistance as a function of temperature. Create separate graphs for the warming-up and cooling-down processes. You may use computer-generated graphs in your report for this lab, or you may plot them by hand.
If you wish to make plots on the computer, you may do so within the Logger Pro program. Keep in mind:
You may also export your dataset to another program and make plots with it, if you wish. You should consider saving each "run" to a floppy disk. Do not save your file on the computer's hard drive. Save As produces a file which can later be opened by Logger Pro
Data may be exported as a text file to be used in other applications. The best way to do this is to cut-and-paste: click on any entry in the Data Table area in Logger Pro, then ¨Select All" and "Copy" from the Edit menu. Open another program (such as Excel or Notepad) and "Paste" the columns of data into it.
Logger Pro's command Export should produce a nice simple ASCII text file with all the data ... but it appears to ignore some of the data columns!
Make a plot of resistance vs. temperature on linear graph paper. Fit a line to the data on this graph, preferably with some computer program that makes a least-squares fit using many data points. From the slope of this line and its vertical intercept at T0, determine R(T0) and the temperature coefficient of resistivity a. In your report you should compare your value for a with that found in your textbook. There should be close agreement between these values, but slight differences can occur. To improve the mechanical strength of wire, copper is usually alloyed with small amounts of other metals. The temperature coefficients of resistivity for these other materials are similar to that for copper.
Calculate the temperature at which the resistance is zero, assuming that the linear relationship you have found remains valid for extended temperature ranges. Comment on this value -- how does it compare to the value of "Absolute Zero" quoted in your textbook?