Download Temperature Dependence of Resistance

Laboratory #4
Name:
Phys 1402 – Dr. Cristian Bahrim
Temperature Dependence of Resistance
When a potential difference is applied across a resistor, a current will
suddenly flow through the resistor from a point of high potential to a point of low
potential. We define the resistance as being the ratio between the potential
difference V (voltage) and the current i through the resistor:
R=
V
.
i
[1]
The resistance of a material depends on many factors, one of the most
important being the temperature. For many materials, such as conductors, the
relationship between T and R is fairly linear over a wide range of temperatures. It
can be written:
R = Ro [ 1 + α (T − To )]
[2]
where α is the temperature coefficient of resistivity. In equation [2], To is the
reference temperature (i.e. room temperature) for the definition of α, and Ro is
the resistance at To. As the temperature increases the atoms within the metal
vibrate with increasingly greater amplitudes, making more difficult for conduction
electrons to travel through the metal. Larger the amplitude of vibration of the
atoms, more resistance the metal opposes to the flow of electrons.
For semiconductors, the resistance decreases with the temperature.
Certain semiconductors, such as pure silicon, at room temperature have such
high resistance that it is effectively an insulator. This is because there are very
few conduction electrons ready to move under the action of a potential difference
and form an electric current. However, by strongly increasing the temperature,
the number of conduction electrons significantly increases, and therefore, for the
same voltage V, the electric current i, in the semiconductor will increase. In this
case, according to eq. [1], the resistance decreases.
In this lab, you will observe the difference in the temperature dependence
of a conductor (the tungsten filament of a light bulb) and a semiconductor (the
carbon filament of a light bulb).
The electric circuit used in this
experiment includes a light bulb of
resistance R (it is the resistance of
the filament), an ammeter, A, a
voltmeter, V, and a power supply
(VARIAC):
A
R
V
V A R I A C
1
In order to plot the resistance of the filament versus temperature,
R = f (T ) , we need to find a way to get information about the temperature of the
filament. Experimental studies about glowing objects proved that the power
radiated (which is the energy radiated per unit time) by a hot object is
proportional with the temperature, i.e. a hotter object radiates more power. The
exact relationship is known as the Stephan – Boltzman’s law
P =σ AT 4
[3]
where σ is a constant and A is the surface area of a glowing object. The equation
(
1/ 4
[3] suggests that a plot R = f (T ) is equivalent with R = f P
). In other words
1/ 4
the equation [3] helps to use P
as a substitute for T. Assuming that all the
electrical energy absorbed by the filament from the VARIAC goes into radiation,
the power radiated can be calculated as:
P =V i
[4]
What to do?
In order to plot the temperature dependence of the light bulb’s
resistance, you need to measure the voltage, V, across the light bulb (with
a voltmeter) and the electric current, i, through it (with an ammeter).
Calculate the power radiated (using equation [4]) and the resistance, R, of
(
1/ 4
the light bulb (using equation [1]), and next, plot R = f P
tungsten (conductor) and carbon (semiconductor) light bulbs.
) for both
Fill the table:
V [V]
i [A]
tungsten
carbon
P [W]
tungsten
P1/4
R[Ω]
carbon
20
40
60
80
100
120
2
tungsten
carbon
tungsten
carbon
Steps to follow for plotting R versus T:
a. Open a Microsoft Excel session.
b. Write the values for voltage V, and current i, you have measured for the
conductor in two separate columns on a worksheet.
c. Calculate on separate columns the values for resistance R, power P,
and P1/4. You can do this either by using your scientific calculator and
writing the values in tables, or, calculate using Excel (your instructor can
shown you the basic commands.)
d. You need to plot R versus P1/4. For plotting data follow the steps:
-
Select the column with values for R.
-
Go on Insert, Chart. It will open the “Chart Wizard” window.
-
Select XY (Scatter) for “Chart Type” and click Next.
-
The “Data Range” for the vertical axis of the plot is already
selected.
-
In the same window with “Data Range” click on “Series” and go to
1/4
“Category (X) axis labels”. Select the column for P
-
and press Next.
Fill out “Chart Title” with the word Conductor, “Category (X) axis”
with Temperature, and “Value (Y) axis” with Resistance.
-
Press “Finish”.
-
Place the plot below the table.
e. For a semiconductor, open another worksheet and repeat the steps b-d.
On the “Chart title” write Semiconductor.
f. Save the Excel file on a floppy disk and print out the two plots.
Each student should have a copy of these plots.
3
Solve the following exercise:
At room temperature (20°C), a light bulb with a carbon filament has a
resistance of 200 Ω. The light bulb is connected to a power supply. An ammeter
of negligible resistance is wired in series with the light bulb. After 10 minutes, the
electric current measured by the ammeter is 1% larger than when the light bulb
was turned on.
(a) What is the temperature of the filament at this moment?
(b) Find the change in the resistance of the light bulb due to the increase
in temperature.
The temperature coefficient of resistivity for carbon is -5 x 10-4 °C-1, at To = 20 °C.
4