Question

Describe clearly an experiment in which you could determine the resistivity of a material. The materials include ammeters, voltmeters, batteries, connecting wires, and multiple pieces of wire made of the unknown material, each with different length and cross-sectional area, electronic balance, diffraction grating, a ruler, a caliper and an air track. The resistivity must be obtained as the slope of a graph. What quantities should be plotted along the axes?

Answer 1

Resistance of a given wire is related to the length and cross-sectional area as:

where r is the radius of the wire.

here, is the resistivity of the material which varies with every material.

the resistance equation can be re-written as:

so, for a given wire with a constant cross sectional area, changing the length of the wire will alter the resistance offered by the wire and their ratio will be such that it remains constant (thus resistivity remains constant).

Experimentally, one must alter the length of the wire and measure the resistance of the wire. For a determined area, plot RA vs L and the slope of the graph will give the resistivity.

To measure Resistance R, connect a small piece of the given material wire in series with the connecting wires and an ammeter in a circuit. The ammeter will measure the current through the wire.

Now connect a voltmeter across (parallel to) the wire. Fix a length L of the wire, and measure Voltage V and current I. Using Ohm's law, the resistance of the wire will be: R = V/I

Now, measure the cross sectional area of the wire. One can do this by either a Vernier Calliper or a Screw Gauge. This reading will give the diameter of the wire. The area will then be:

multiply this with the determined value of Resistance for a fixed length L. Repeat this process for different lengths of the wire.

Plot RA on y axis and L on x axis. The slope of such a graph will determine the unknown resistivity of the wire.