# Purpose

To determine how the resistivity depends on the length and the cross sectional area of the resistor.

# Objectives

• To learn how to use Ohm’s Law to determine the resistivity of an object
• To learn how to organize and analyze experimental data in spreadsheets
• To learn how to use linear regression to fit experimental data
• To learn how to plot experimental data and interpret the graph in physics terms.
• To be able to find relevant information by reading through equipment manuals

# Pre-lab Activity

If you have not worked with multimeters before, go to the Instrumentation page and become familiar with how they work.

Assignment: Take the following safety quiz.  You have unlimited attempts, but you must get perfect score.

Go through Pasco’s Resistance Manual and record the resistivity and the diameter of the wire for each of the following three materials. Note, there are brass wires with four different diameters.

 Material Resistivity (Ω.cm) Diameter (cm) Copper Aluminum Brass Brass Brass Brass

# Theory

The resistance of a wire is given by:

$R=\rho \frac{L}{A}$

Here R is the resistance of the wire in Ω , ρ is the resistivity of the material, L is the length of the wire, and A is the cross sectional area of the wire.  Wires are typically cylindrical, so their cross sectional area is:

$A = \pi R^2$

# Experimental Settings

Connect the Universal 850 Pasco Interface, the galvanometer, and the Resistivity Apparatus as shown in the Pasco Manual.

Break the red wire and connect a Digital Ammeter in series with the apparatus. The Ammeter will be measuring high currents, so you must use the 10A input. Set the range to 10 A.

Go to Pasco Capstone software and set up the Input for DC current with amplitude of 2.0 V.  Set up the galvanometer and click and drag a table to show the voltage measured by the galvanometer.

Ask your instructor to check your circuit. Then, turn on the power within the Pasco Capstone software. You are ready to take measurements.

# Experimental Data and Results

In a spreadsheet, record your measurements for the current and voltage for the following lengths of the wire: 8 cm, 12 cm, 16 cm, 20 cm, and 24 cm.

Calculate the resistance for each length and plot it versus the length of the wire, R vs. L.

Use linear regression to determine the best linear fit. Calculate the slope of the best fit line and determine the resistivity of the wire from the slope.

Compare the resistivity with the value published in the Pasco manual (see your pre-lab activities).