Download Finding the Temperature of a Light Bulb Filament

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Union College
Fall 2015
Physics 121
Lab #6: Ohmic and Non-ohmic Devices, or Finding the Operating Temperature of a Light
Bulb Filament
Introduction. Two important concepts about resistors that you have been told (in class and in
the text) are:
1. The resistance of a device in a circuit depends on the material of which it is made and on its
size and shape. In particular
(1)
R  L / A ,
where 𝜌 is the resistivity of the material, L is the length of wire in the resistor, and A is the crosssectional area (𝐴 = 𝜋𝑟 2 for a circular cross-section). The resistivities of various materials are
given in the attached table.
2: Ohm’s law, which says that for most resistors there is a simple relationship between the
current through the resistor and the voltage difference applied across the ends, i.e.
(2)
V  IR .
Resistors for which Ohm’s law works for a large range of voltages are considered ohmic. With
some devices, however, the relation between V and I may deviate a bit from this simple linear
relation. Often this is because a larger current heats up the resistor and for most materials a
substantial change in temperature causes a change in resistivity. The temperature dependence of
resistance typically follows the following equation
(3)
R  R0 [1   (T  T0 )] ,
where R0 is the resistance at temperature T0 and 𝛼 is a property of the resistive material called
the temperature coefficient of resistance. In this lab, you will measure the changing resistance of
a light bulb filament as it gets hotter and obtain a measure of the filament’s temperature when it
is glowing.
Procedure:
A. Resistance: The large copper coil at your station has 3400 turns of copper wire. Since the
wire is completely enclosed in the apparatus, it is difficult to measure the diameter of the wire.
We will use an indirect method (using Equation (1)) to find the diameter of the wire.
1) First, by visual comparison with the millimeter markings on the ruler, make your best
estimate of the diameter of the wire.
2) Use the DMM to measure the resistance of the coil. (Use the “COM” and “V  ” receptacles
in the DMM and turn the dial to the “  ” setting. Note for future info: When measuring
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resistance, the device whose resistance you wish to measure should be disconnected from
the circuit.)
3) Use a ruler to measure the inner and outer diameters of the coil and find the average. Then
estimate the total length of the wire based on the average radius. (Recall that C = 2R.)
4) Refer to the attached table to find the resistivity of copper and use Equation (1) to calculate
the radius of the wire. How does this compare with your estimate?
B. Ohm’s Law and the operating temperature of the light bulb.
1) Use the DMM to measure (and record in Excel) the resistance of the
ceramic resistor.
2) Measure and record the resistance of the light bulb.
3) Connect the ceramic resistor and light bulb into the series circuit, as
shown in figure.
Measuring Voltage and Current:
In this experiment, you will be measuring voltage across and and current through each of these
two circuit elements for a range of power supply settings. You will, therefore, need to connect
and reconnect the meters. Here, then, are some instructions to read first about using the DMMs
as volt meters and ammeters.
Current: Important: ALWAYS MAKE SURE THAT AN AMMETER, WHEN BEING
CONNECTED TO AN ACTIVE CIRCUIT, IS CONNECTED IN A LINE WITH SOME
RESISTANCE, I.E. NEVER CONNECT AN AMMETER IN PARALLEL! Strictly speaking,
an ammeter measures the current going through the meter itself. We measure the current going
through a resistor by inserting the meter properly into the circuit just before or just after the
resistor. The basic idea is that, by the node rule, the ammeter and the resistor have the same
current going through them. In order for the ammeter to not alter the amount of current going
through the resistor, it must have negligible resistance. Therefore, when you set your DMM dial
to measure current (especially the “mA” setting), and place the plugs into the “COM” and “mA”
receptacles, the meter is vulnerable to large currents passing through it. If you were to hook up
an ammeter directly to a power supply, for example, the amount of current that would pass
through it would destroy it. For that reason, the ammeter has a fuse as part of its current-setting
circuit and the fuse blows whenever the current gets above a certain threshold. If you were to
hook the ammeter in parallel with the resistor, since the ammeter has insignificant resistance, all
the current would go through the ammeter and not the resistor, and the fuse will blow. If the fuse
is blown your ammeter will register 0.00 amps, regardless of what it should be.
To measure the current through a resistor, first turn off the power, then disconnect the circuit just
before the resistor, move the lead to the DMM “COM” receptacle, and then add a new lead from
the “A” receptacle to the resistor. Turn the dial to “A.” If the current is too small, move the lead
to the “mA” receptacle and turn the dial to the “mA” setting.
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Direction of current. The positive or negative reading of current in the multimeter indicates the
direction of the current. The meter will give a positive reading if the current passes through the
meter from the “mA” receptacle to the “COM” receptacle.
Voltage: Make sure that the meter is not set up to measure current BEFORE connecting it to the
circuit (or you’ll blow the fuse). Turn the dial to read “V” and insert the cords’ plugs into the
“COM” and “V” receptacles. Then, connect the other ends of the cords to the circuit on either
side of the resistor. (The voltmeter, then, is connected in parallel with the resistor).
4) Arrange the DMMs to measure the current through and voltage across the resistor. Have
your instructor inspect your circuit before continuing. Turn the power supply on and set
its output voltage to 5V, and read the current and voltage values on the meters.
5) Vary the voltage of the power supply in roughly 3V increments, from zero to 15V (the
voltage settings don’t need to be exact). In each case record the voltage and current Excel.
Plot a V vs I graph for the resistor (V on the vertical axis), add a linear trendline that goes
through the origin and include the equation of the line on the graph. Do a regression to
obtain an uncertainty in the slope.
6) What resistance does the slope indicate in Ohms? How does this compare with the resistance
value you measured when the resistor was separate from the circuit? Are they consistent
considering the uncertainty in the slope? Calculate the percent difference.
7) Now move the DMMs to read the current through and voltage across the light bulb. Have
your instructor inspect the circuit first, and measure the current and voltage for the same set
of power supply voltages as for the resistor. Watch carefully and take note of the current
when the bulb first begins to glow faintly red. Plot a graph of V vs I for the light bulb. What
is the principle difference you see between the two graphs? Fit a linear trendline that goes
through the origin. How does the slope compare with the measured resistance (from step
3)? How well does the line fit to the data?
8) Characterize each device by how close they are to being ohmic, at least in terms of the range
of measurements you made. If non-ohmic, estimate the slope of the plot at the high current
end and calculate the amount of deviation from Ohm’s law, i.e., how much does the
resistance given by V/I differ from the measured resistance when the device is disconnected
from the circuit? What is the percent difference?
9) Re-arrange Equation (3) to give an expression for T, and make another column in Excel that
calculates the temperature of the filament for each set of V and I. Use the temperature
coefficient of Tungsten from the attached table, and let T0 and R0 equal room temperature
and the resistance you measured when the filament was disconnected.
10) According to these results, what is the temperature of the filament when it first starts to glow
red? What is its temperature when it was brightest (i.e. when it had the largest current)?
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