Experiment III

Thermistors and the Wheatstone Bridge

**Introduction**

By the use of the Wheatstone bridge, a type of null comparator, the
temperature versus resistance behavior of a thermistor is plotted. Using
this calibration curve, one's body temperature is determined.

**Equipment**

Galvanometer, 2-known resistors, 0 - 999 W
decade resistance box, thermistor, wires, rubberbands, Bunsen burner, beaker,
and thermometer .

Note: Bring linear graph paper.

**Theory**

When a meter is used for measuring electrical circuits, the meter must
draw some power from the circuit to make the measurement. This effect is
known as "loading" of the circuit by the meter.

For an ammeter the loading has the effect of adding a series resistance
to the circuit. For a voltmeter the effect is of a parallel resistance.
Thus, for a voltmeter, the greater its input resistance (or impedance in
the A.C. case), the better the measurement. However, even the best PET-digital
meters, with input impedances greater than 10 MW
or 10´10^{6} W
, pull *some* power, though usually negligible, from the circuit.

To circumvent the loading problem, null comparators are used. Null comparators
make a measurement by comparing two quantities, one of known value, the
other unknown. The known value is adjusted till it equals the unknown.
When they are equal, a detector placed across them will give a zero reading.
Hence the term, null comparator.

A voltmeter, or a galvanometer can be used as the detector, as when
two points are at the same voltage, no current will flow between them.
As the measurement is made when the meter is nulled, no loading occurred.
Hence the accuracy of the measurement is limited only by the knowledge
of the known quantity, and the sensitivity of the nulled detector.

The Wheatstone bridge is a null comparator used for very accurate measurement of resistance.

In the Wheatstone
bridge of Figure 3.1, R_{1}, R_{2}, and R_{3} are
known resistances, R_{x} is the unknown. The bridge is said to
be balanced when P_{l} is at the same potential as P_{2}.
Thus, no current will flow through the galvanometer. For this to happen,
the ratio of resistance in the R_{l} - R_{2} path must
equal the ratio in the R_{3} - R_{x} path:

Thus, if R_{2}, is twice the value of R_{1}, then R_{x}
is twice R_{3}, or

A thermistor is a metal oxide semiconductor whose resistance varies
with temperature. For a conductor, as its temperature is increased, its
resistance will increase. However, the resistance of a semiconductor will
decrease with an increase in temperature. Over a wide range of temperature,
this change in resistance is very non-linear. However, in a restricted
range of 10° C or less, it may appear fairly
linear. Because of this, thermistors are employed in a wide range of applications
as temperature sensors.

In this experiment, you will measure the resistance of a thermistor
with a Wheatstone bridge, for different temperatures, in a water bath.
Then you will plot a calibration curve and use the thermistor to find your
body temperature.

**Procedure**

Wire the circuit as in Figure 3.3, using the 0-999 W
decade box for R_{3}:

You will balance
the bridge by varying the decadebox, till the galvanometer indicates no
current is flowing. For the initial rough balancing, the resistor switch
SW_{1} should be *open*. This adds a series resistance to
the galvanometer to protect it from too much current when unbalanced. Once
the bridge is roughly balanced, fine-balance it by closing SW_{1}.
This shorts around the resistor, giving full sensitivity of the galvanometer.

Attach the thermistor to the Hg thermometer with a rubber band. Place
in a water bath brought to 0°C with a little
ice. *DO NOT* stir with the thermometer, as it is fragile, and will
break.

Heat the bath slowly with the Bunsen burner. Be careful not to melt
the wires in the flame. *DO NOT* place the thermistor in the flame
to see what happens! To do so will ruin the thermistor and your chances
of passing this course.

Record the resistance of the thermistor in 10°C
steps, from 0°C to 100°C.
Uae the computer program "Quattro Pro and plot your data with temperature
on the abscissa and resistance on the ordinate.

You may find it difficult to fit a straight line to your data. This
is because, as many things in nature, the resistance varies as an exponential.
For a semiconductor, the resistivity depends on the inverse of the *absolute
temperature* (Kelvin), or

r µ e^{K/T}

If the thermal expansion in the thermistor is neglected, then the above
equation can be written in terms of resistance, or

R µ e^{K/T}

To make an equation of this relationship, multiply by a constant to
yield

R = Ce^{K/T}

By taking the natural log of both sides, we have a linear equation in ln R and 1/T:

Redefining C' to be the constant ln C, we have

or y = b + mx.

Plot the natural log of the resistance versus the inverse of the temperature
(*in Kelvin*) using the "Quattro Pro" template. Follow the
instructions given in the template and draw a "best-fit" straight
line to your data. Measure the resistance of the thermistor at body temperature
by holding the thermistor between your lower and upper arms. *Then, using
this calibration curve, determine your body temperature, giving your answer
in°C and°F.
*

The slope of the semi-log plot is related to the energy gap (E_{g})
of the semiconductor (thermistor). (The semiconducting gap is the region
where no electrons are allowed and is between the valence and conduction
bands.) Find the slope, m, and calculate the semiconducting gap using the
following relation

m = E_{g}/2k_{B}

where k_{B} = 1.38×10^{-23} J/K is the Boltzmann's
constant. Give your answer in J and in eV where 1 eV = 1.6 × 10^{-19}
J. (Note: The slope of thesemi-log plot is obtained by performing a "linear
regression fit" to your data points. Question: What is the unit of
the slope?)

Answer the following questions and include with your report:

1. What are the major factors limiting the accuracy of a null Comparator?

2. If you wished the Wheatstone bridge to be direct-reading, *i.e.*,
the value given by the decade box R_{3} to be the same as R_{x},
what must be the values of R_{l} and R_{2}?

3. If a RTD (Resistive Thermal Device, made of ordinary conductor) were used instead of a thermistor, how would the calibration curve differ?

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This page last updated on December 30, 1996.

© 1996 Dr. H. K. Ng.

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