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PHY136H5 (11)


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Wagih Ghobriel

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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