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Physics
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PHY136H5
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Wagih Ghobriel
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Lecture

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Physics

PHY136H5

Wagih Ghobriel

Winter

Description

EXPERIMENT
TEMPERATURE DEPENDENCE OF RESISTIVITY
Introduction:
When a battery is connected across a resistor (e.g. a light bulb or a heating element), current
will flow through it. How much current is determined by a property of the resistor called (naturally) its
resistance. The larger the resistance, the smaller the current.
What determines the resistance of an object? Among other things, it depends on what the object
is made of. For example, identical cylinders of copper and rubber will have vastly different resistances
to current flow. Copper is a good conductor whereas rubber is a good insulator. They differ in a
property called the resistivity. Resistivity is a microscopic parameter which depends on the interaction
between the current-carrying electrons and the lattice.
The microscopic origin of resistivity is easy to picture. As an electron travels through a lattice,
it will interact with, and be scattered by, the lattice ions. In other words, the lattice will interfere with
the flow of the electrons.
In general, resistivity is a function of temperature. In normal metals, resistivity tends to increase
with temperature as the increased thermal motion of the lattice further obstructs the electron flow. In
some semi-conductors, the resistivity actually decreases with temperature. In such materials, the effect
of temperature is to make more electrons available for conduction.
In this experiment you will investigate the temperature dependence of this fundamental
parameter in a variety of materials. In Exercise 1 you will practice measuring resistance using a
Wheatstone bridge. Then in Exercise 2 you will use the bridge to measure the resistance of several
samples while heating them.
Exercise 1:
R X
The Wheatstone bridge C
circuit is shown in Fig.1. An
unknown resistor, X, is placed in
series with a variable, but known G
resistor R. The resistor AB is
simply a wire of uniform cross- A a D b B
sectional area. Its resistance is
divided into two parts,aR and b , Ra Rb
by the sliding contact D. Since the
resistance of a wire is proportional
to its length, the magnitude oa R
and Rbdepend on the contact point
along the wire. For example, let Figure 1: Wheatstone Bridge
the total resistance of the slide
wire be R0. 2
Then
if the contact D is at A : R = 0 , R = R
i) a b 0
ii) if the contact D is at B : R a R ,0R =b0
iii) if the contact D is in the middle R a R =b½ R 0
More generally
R b b
(1)
R a a
where a and b are the lengths of a and Rb, respectively.
A galvanometer, G, measures the current flow between the points C and D. The bridge is said
to be balanced when the current is zero. When the bridge is balanced, the value of the unknown
resistor X can be calculated as:
X R Rb R b (2)
Ra a
In this part of the experiment, you can practice using the bridge by measuring the resistance of
some standard carbon resistors. Set up the circuit according to the schematic diagram in Fig.2. Connect
the power supply, P, the resistance box, R, and a carbon resistor, X, to the binding posts as shown.
Attach one terminal of the galvanometer, G, to the binding post in the center on the metal strip, and the
other to the contact key, K, which slides along the wire. The key must be depressed in order to close
the circuit. Take care to avoid loose connections.
Begin by finding an approximate value for the resistance X. Set the slider to the center of the
slide wire and momentarily depress the contact key for various values of R. Note where the polarity of
the readings changes: the value of X must be somewhere between these two R values. (Do you
understand why?)
0
GALVANOMETER G
Decades Resistance
Box Unknown
R X Resistor
Contact Key K Metal Strip
Slide Wire
a b
Power Supply P
Figure 2: Schematic Diagram of the Equipment Setup 3
To find a more accurate value of X, choose one of the R values on either side of the polarity
change. Move the slider along the wire until the galvanometer shows a zero deflection. This is the
balance point. You can increase the sensitivity of the apparatus by depressing the button on the face of
the galvanometer to magnify the scale. Try 5-10 different values of R and record the values of a and b
for each. Plot R vs a/b and find X by extracting the slope. Replace X with a second carbon resistor, and
repeat this procedure for the new value of X. When considering the uncertainty, the normal regression
method may yield an overly small value. As such, consider the following:
From Eq.(2) and the rules for propagation of errors, the uncertainty in X is
2 2 2
X X R R a R b (3)

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