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Course 1 Laboratory
Second Semester
Module: Lamp Filament
Units:1
1
Characteristics of a Lamp Filament
1 Introduction
This experiment will give you some practice in measuring resistance using a technique
introduced in the first semester experiment "D.C. Resistance Measurements". You will
determine the resistance of the tungsten filament of a small indicator lamp as a function
of the power supplied to it. The filament resistance increases as the temperature rises
and from your measurements of resistance you can determine the temperature of the
filament and, hence, you will be able to investigate the relationship between temperature
and power dissipated by the filament.
2 Basic Theory
When a light bulb is switched on its filament quickly attains thermal equilibrium such
that the electrical power supplied to the bulb is dissipated as heat by conduction,
convection and radiation.
Radiation ∝ T4
Figure 1. The emission of
thermal energy from a
filament via the process
of radiation and
conduction.
Conduction ∝ T
Filament
When the filament glows red or white hot, radiation losses dominate. If conduction and
convection losses are neglected then the electrical power P and the filament absolute
temperature T should satisfy the T4 radiation law:
P = σεA (T4 − T04),
(1)
where σ is Stephan's constant, ε is the emissivity of tungsten (which depends on the
nature of the surface of the material), A is the surface area of the filament, and T0 is the
temperature of the surroundings. The emissivity determines how good a material is at
radiating and absorbing photons (electromagnetic radiation). You are asked to
investigate to what extent this simple equation describes the behaviour of your lamp
filament as the power is increased from a few milliwatts up to a maximum of about
300mW.
The electrical power P supplied to the filament can be calculated from its resistance and
the voltage drop across it. Determination of the filament temperature T is less obvious
but relies on the fact that the temperature dependence of the resistivity of tungsten has
been measured separately, and above 300 K is given by
Temp = 77.61 +
R
R300
 R

 R

0.28 − 7.03
+ 234.78
 R300
  R300

2
( 2)
You will need to determine accurately the room-temperature resistance of your filament
as described in section 4 and the resistance at 300 K. The conversion of resistance to
temperature is explained in detail in section 5.
3 Experimental Details
You are supplied with a small 6V (maximum) indicator bulb whose resistance varies
from about 10Ω at room temperature to around 100Ω at full power. The accurate
measurement of small resistances is discussed in the manual on "D.C. Resistance
Measurements".
For this experiment the arrangement shown in Figure (2) is
recommended - explain why. The filament of resistance RL is connected in series with
a standard resistance RS; the circuit is driven by a D.C. power supply. A changeover
switch is used to switch a digital voltmeter between reading the voltage VL across the
filament resistance RL and the voltage VS across RS. Since the current, I, flowing
through Rs and RL is the same, it follows that
RL =
VL
R
VS S
(3)
and the power dissipation in the filament is
P = IVL =
VLVS
RS
.
(4)
As usual with D.C. measurements, a reversing switch is included so that a check can be
made for thermal e.m.f.'s. A resistance box is supplied for use as RS: a value of about
400Ω is sensible to prevent the filament voltage from exceeding 6V.
Changeover
Switch
A
B
DVM
Lamp
Power
Supply
RS
Reversing Switch
Figure 1
4 Procedure
Connect up the circuit shown in Figure (2). If in doubt ask a demonstrator to check the
circuit for you. Then proceed as follows:
3
4.1 Low Temperature Run
You will need to know the resistance of the filament at room temperature, and the
obvious way to find this is to pass a very small current through it. However, even a
small current produces a measurable increase in filament resistance, therefore it is a
good idea to measure RL as a function of power and then to extrapolate to zero power.
Measure VL and VS as accurately as possible using the DVM and then use equations (3)
and (4) to calculate RL and P. Quite small powers should be used (up to about 2mW,
causing the filament resistance to rise to about 20Ω). Do not forget to record room
temperature as well!
4.2 Main Run
Equation (1) is the power verses temperature law to be expected when radiation losses
dominate once the filament is very hot. Measure VL and VS for a dozen or more fairly
evenly spaced different powers at filament voltages from about 2V up to the maximum
of 6V. Remember to note down the value of RS. If time permits, take a few readings for
lower powers, but be sure to leave yourself at least two hours for analysing the results
as described in the next section.
Analysing the Results
4.3 Determination Of The Room-Temperature Resistance
Plot a graph of filament resistance verses power using your results from the lowtemperature run. You should find that RL varies linearly with P at the low powers used
here.
What is the dominant mechanism of heat loss in this regime?
Use the Mathcad least-squares straight-line fitting program to extrapolate to zero power
and hence obtain an accurate room-temperature value of RL along with its standard
error.
4.4 Determination Of The Filament Temperature
The resistivity of tungsten as a function of absolute temperature T is tabulated in the
reference as ρ(T)/ρ(300). You have measured the filament resistance R and will deduce
T from the resistance ratio R(T)/R(300).
There is in fact a small difference between these two ratios, which you can estimate
given that the linear expansion coefficient of tungsten is about 6×10-6 C-1, since
R=ρ
l
A
and
ρ (T ) l (T )
R (T )
=
.
R (300) ρ (300) l (300)
Is this correction significant?
The resistance of the filament at 300K must first be calculated from your roomtemperature value. For this small extrapolation, the linear relation
RL(θ) = RL(0) (1 + αθ)
4
(5)
can be used, where θ is the temperature in degrees centigrade, RL(θ) and RL(0) are
resistances at θ°C and 0°C, and α=5.238×10-3 deg-1 C.
Once you have calculated RL(300) the spreadsheet called filament.mcd can be used
to convert filament resistance obtained in your main run to absolute temperature. Enter
your value of RL(300) at the start. Entering your higher values of RL and will then give
you values of T from equation (2) (and also T4).
4.5 Verification of the T4 radiation law
You can now check the validity of the T4 radiation law assumed in equation (1). First
plot the results from your main run as power verses T4.
Is this graph a straight line? It may well be curved at the lowest powers: can you think
of any reasons why?
The graph ought to be reasonably straight for T above about 1000°C, use only these
higher-temperature points in the analysis.
From the gradient and intercept deduce values for ε and T0, taking the filament to be a
cylinder of length 1.84mm and diameter 0.133mm.
Are the values you obtain reasonable?
Finish your account by writing a short summary of your results.
5 Reference
Langmuir and Jones, "Properties of Tungsten" in Handbook of Chemistry and Physics,
53rd edition, page E214. (see also 72nd Ed)
5